[{"date_published":"2022-03-26T00:00:00Z","_id":"10765","oa":1,"author":[{"first_name":"Yang","full_name":"Cao, Yang","last_name":"Cao"},{"last_name":"Huang","id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","full_name":"Huang, Zhizhong","first_name":"Zhizhong"}],"type":"journal_article","year":"2022","publisher":"Elsevier","doi":"10.1016/j.aim.2022.108236","language":[{"iso":"eng"}],"volume":398,"article_type":"original","isi":1,"publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"quality_controlled":"1","month":"03","intvolume":"       398","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"TiBr"}],"acknowledgement":"We are grateful to Mikhail Borovoi, Zeev Rudnick and Olivier Wienberg for their interest in our\r\nwork. We would like to address our gratitude to Ulrich Derenthal for his generous support at Leibniz Universitat Hannover. We are in debt to Tim Browning for an enlightening discussion and to the anonymous referees for critical comments, which lead to overall improvements of various preliminary versions of this paper. Part of this work was carried out and reported during a visit to the University of Science and Technology of China. We thank Yongqi Liang for offering warm hospitality. The first author was supported by a Humboldt-Forschungsstipendium. The second author was supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft.","date_created":"2022-02-20T23:01:30Z","article_number":"108236","abstract":[{"lang":"eng","text":"We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate integral quadratic form in  n>3 variables and m is a non-zero integer. This gives asymptotic formulas for the density of integral points taking coprime polynomial values, which is a quantitative version of the arithmetic purity of strong approximation property off infinity for affine quadrics."}],"day":"26","publication_status":"published","oa_version":"Preprint","status":"public","date_updated":"2023-08-02T14:24:18Z","title":"Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics","external_id":{"arxiv":["2003.07287"],"isi":["000792517300014"]},"publication":"Advances in Mathematics","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2003.07287"}],"scopus_import":"1","issue":"3","citation":{"ieee":"Y. Cao and Z. Huang, “Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics,” <i>Advances in Mathematics</i>, vol. 398, no. 3. Elsevier, 2022.","chicago":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.aim.2022.108236\">https://doi.org/10.1016/j.aim.2022.108236</a>.","ama":"Cao Y, Huang Z. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>. 2022;398(3). doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108236\">10.1016/j.aim.2022.108236</a>","ista":"Cao Y, Huang Z. 2022. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. Advances in Mathematics. 398(3), 108236.","short":"Y. Cao, Z. Huang, Advances in Mathematics 398 (2022).","apa":"Cao, Y., &#38; Huang, Z. (2022). Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2022.108236\">https://doi.org/10.1016/j.aim.2022.108236</a>","mla":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>, vol. 398, no. 3, 108236, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108236\">10.1016/j.aim.2022.108236</a>."},"arxiv":1},{"publication_identifier":{"issn":["0001-8708"]},"quality_controlled":"1","month":"10","volume":408,"article_type":"original","isi":1,"department":[{"_id":"VaKa"}],"acknowledgement":"We are grateful to a number of colleagues for helpful and inspiring discussions during the time when we worked on this project, in particular Dima Dudko, Misha Hlushchanka, John Hubbard, Misha Lyubich, Oleg Kozlovski, and Sebastian van Strien. Finally, we would like to thank our dynamics research group for numerous helpful and enjoyable discussions: Konstantin Bogdanov, Roman Chernov, Russell Lodge, Steffen Maaß, David Pfrang, Bernhard Reinke, Sergey Shemyakov, and Maik Sowinski. We gratefully acknowledge support by the Advanced Grant “HOLOGRAM” (#695 621) of the European Research Council (ERC), as well as hospitality of Cornell University in the spring of 2018 while much of this work was prepared. The first-named author also acknowledges the support of the ERC Advanced Grant “SPERIG” (#885 707).","article_number":"108591","date_created":"2022-08-01T17:08:16Z","intvolume":"       408","keyword":["General Mathematics"],"file_date_updated":"2023-02-02T07:39:09Z","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","_id":"11717","oa":1,"author":[{"last_name":"Drach","id":"fe8209e2-906f-11eb-847d-950f8fc09115","orcid":"0000-0002-9156-8616","first_name":"Kostiantyn","full_name":"Drach, Kostiantyn"},{"full_name":"Schleicher, Dierk","first_name":"Dierk","last_name":"Schleicher"}],"date_published":"2022-10-29T00:00:00Z","year":"2022","publisher":"Elsevier","doi":"10.1016/j.aim.2022.108591","language":[{"iso":"eng"}],"type":"journal_article","title":"Rigidity of Newton dynamics","file":[{"date_updated":"2023-02-02T07:39:09Z","success":1,"date_created":"2023-02-02T07:39:09Z","checksum":"2710e6f5820f8c20a676ddcbb30f0e8d","file_id":"12474","file_size":2164036,"file_name":"2022_AdvancesMathematics_Drach.pdf","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst"}],"external_id":{"isi":["000860924200005"]},"publication":"Advances in Mathematics","citation":{"ieee":"K. Drach and D. Schleicher, “Rigidity of Newton dynamics,” <i>Advances in Mathematics</i>, vol. 408, no. Part A. Elsevier, 2022.","chicago":"Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” <i>Advances in Mathematics</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.aim.2022.108591\">https://doi.org/10.1016/j.aim.2022.108591</a>.","ama":"Drach K, Schleicher D. Rigidity of Newton dynamics. <i>Advances in Mathematics</i>. 2022;408(Part A). doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108591\">10.1016/j.aim.2022.108591</a>","apa":"Drach, K., &#38; Schleicher, D. (2022). Rigidity of Newton dynamics. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2022.108591\">https://doi.org/10.1016/j.aim.2022.108591</a>","mla":"Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” <i>Advances in Mathematics</i>, vol. 408, no. Part A, 108591, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108591\">10.1016/j.aim.2022.108591</a>.","short":"K. Drach, D. Schleicher, Advances in Mathematics 408 (2022).","ista":"Drach K, Schleicher D. 2022. Rigidity of Newton dynamics. Advances in Mathematics. 408(Part A), 108591."},"project":[{"name":"Spectral rigidity and integrability for billiards and geodesic flows","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","call_identifier":"H2020"}],"has_accepted_license":"1","scopus_import":"1","issue":"Part A","abstract":[{"text":"We study rigidity of rational maps that come from Newton's root finding method for polynomials of arbitrary degrees. We establish dynamical rigidity of these maps: each point in the Julia set of a Newton map is either rigid (i.e. its orbit can be distinguished in combinatorial terms from all other orbits), or the orbit of this point eventually lands in the filled-in Julia set of a polynomial-like restriction of the original map. As a corollary, we show that the Julia sets of Newton maps in many non-trivial cases are locally connected; in particular, every cubic Newton map without Siegel points has locally connected Julia set.\r\nIn the parameter space of Newton maps of arbitrary degree we obtain the following rigidity result: any two combinatorially equivalent Newton maps are quasiconformally conjugate in a neighborhood of their Julia sets provided that they either non-renormalizable, or they are both renormalizable “in the same way”.\r\nOur main tool is a generalized renormalization concept called “complex box mappings” for which we extend a dynamical rigidity result by Kozlovski and van Strien so as to include irrationally indifferent and renormalizable situations.","lang":"eng"}],"ec_funded":1,"day":"29","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication_status":"published","oa_version":"Published Version","date_updated":"2023-08-03T12:36:07Z","status":"public"},{"date_published":"2021-03-26T00:00:00Z","author":[{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","first_name":"Daniel"}],"_id":"9036","oa":1,"type":"journal_article","doi":"10.1016/j.aim.2021.107595","language":[{"iso":"eng"}],"year":"2021","publisher":"Elsevier","isi":1,"article_type":"original","volume":380,"month":"03","publication_identifier":{"issn":["0001-8708"]},"quality_controlled":"1","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       380","keyword":["General Mathematics"],"article_number":"107595","date_created":"2021-01-22T17:55:17Z","department":[{"_id":"LaEr"}],"acknowledgement":"D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","day":"26","oa_version":"Preprint","publication_status":"published","abstract":[{"lang":"eng","text":"In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space."}],"ec_funded":1,"status":"public","date_updated":"2023-08-07T13:34:48Z","publication":"Advances in Mathematics","title":"The metric property of the quantum Jensen-Shannon divergence","external_id":{"isi":["000619676100035"],"arxiv":["1910.10447"]},"main_file_link":[{"url":"https://arxiv.org/abs/1910.10447","open_access":"1"}],"issue":"3","citation":{"chicago":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.aim.2021.107595\">https://doi.org/10.1016/j.aim.2021.107595</a>.","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” <i>Advances in Mathematics</i>, vol. 380, no. 3. Elsevier, 2021.","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595.","short":"D. Virosztek, Advances in Mathematics 380 (2021).","mla":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” <i>Advances in Mathematics</i>, vol. 380, no. 3, 107595, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107595\">10.1016/j.aim.2021.107595</a>.","apa":"Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2021.107595\">https://doi.org/10.1016/j.aim.2021.107595</a>","ama":"Virosztek D. The metric property of the quantum Jensen-Shannon divergence. <i>Advances in Mathematics</i>. 2021;380(3). doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107595\">10.1016/j.aim.2021.107595</a>"},"arxiv":1,"project":[{"grant_number":"846294","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability"}]},{"article_number":"107992","date_created":"2021-09-21T15:58:59Z","acknowledgement":"The author would like to express his gratitude to D. Gaitsgory, without whose tireless guidance and encouragement in pursuing this problem, this work would not have been possible. The author is grateful to his advisor B.C. Ngô for many years of patient guidance and support. This paper is revised while the author is a postdoc in Hausel group at IST Austria. We thank him and the group for providing a wonderful research environment. The author also gratefully acknowledges the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization Homology,” Austrian Science Fund (FWF): M 2751.","department":[{"_id":"TaHa"}],"file_date_updated":"2021-09-21T15:58:52Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","ddc":["514"],"intvolume":"       392","keyword":["Chiral algebras","Chiral homology","Factorization algebras","Koszul duality","Ran space"],"month":"09","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"quality_controlled":"1","isi":1,"article_type":"original","volume":392,"doi":"10.1016/j.aim.2021.107992","language":[{"iso":"eng"}],"year":"2021","publisher":"Elsevier","type":"journal_article","author":[{"first_name":"Quoc P","full_name":"Ho, Quoc P","orcid":"0000-0001-6889-1418","last_name":"Ho","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87"}],"_id":"10033","oa":1,"date_published":"2021-09-21T00:00:00Z","arxiv":1,"citation":{"mla":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>, vol. 392, 107992, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>.","apa":"Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>","short":"Q.P. Ho, Advances in Mathematics 392 (2021).","ista":"Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992.","ama":"Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. 2021;392. doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>","chicago":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>.","ieee":"Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” <i>Advances in Mathematics</i>, vol. 392. Elsevier, 2021."},"project":[{"grant_number":"M02751","call_identifier":"FWF","name":"Algebro-Geometric Applications of Factorization Homology","_id":"26B96266-B435-11E9-9278-68D0E5697425"}],"scopus_import":"1","has_accepted_license":"1","publication":"Advances in Mathematics","file":[{"date_updated":"2021-09-21T15:58:52Z","date_created":"2021-09-21T15:58:52Z","checksum":"f3c0086d41af11db31c00014efb38072","file_id":"10034","file_size":840635,"file_name":"1-s2.0-S000187082100431X-main.pdf","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"qho"}],"title":"The Atiyah-Bott formula and connectivity in chiral Koszul duality","external_id":{"isi":["000707040300031"],"arxiv":["1610.00212"]},"date_updated":"2023-08-14T06:54:35Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"21","oa_version":"Published Version","publication_status":"published","abstract":[{"text":"The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5].","lang":"eng"}]},{"status":"public","date_updated":"2023-02-23T14:01:57Z","abstract":[{"text":"Consider the sum  X(ξ)=∑ni=1aiξi , where  a=(ai)ni=1  is a sequence of non-zero reals and  ξ=(ξi)ni=1  is a sequence of i.i.d. Rademacher random variables (that is,  Pr[ξi=1]=Pr[ξi=−1]=1/2 ). The classical Littlewood-Offord problem asks for the best possible upper bound on the concentration probabilities  Pr[X=x] . In this paper we study a resilience version of the Littlewood-Offord problem: how many of the  ξi  is an adversary typically allowed to change without being able to force concentration on a particular value? We solve this problem asymptotically, and present a few interesting open problems.","lang":"eng"}],"publication_status":"published","oa_version":"Preprint","page":"292-312","day":"15","scopus_import":"1","citation":{"ama":"Bandeira AS, Ferber A, Kwan MA. Resilience for the Littlewood–Offord problem. <i>Advances in Mathematics</i>. 2017;319:292-312. doi:<a href=\"https://doi.org/10.1016/j.aim.2017.08.031\">10.1016/j.aim.2017.08.031</a>","short":"A.S. Bandeira, A. Ferber, M.A. Kwan, Advances in Mathematics 319 (2017) 292–312.","apa":"Bandeira, A. S., Ferber, A., &#38; Kwan, M. A. (2017). Resilience for the Littlewood–Offord problem. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2017.08.031\">https://doi.org/10.1016/j.aim.2017.08.031</a>","mla":"Bandeira, Afonso S., et al. “Resilience for the Littlewood–Offord Problem.” <i>Advances in Mathematics</i>, vol. 319, Elsevier, 2017, pp. 292–312, doi:<a href=\"https://doi.org/10.1016/j.aim.2017.08.031\">10.1016/j.aim.2017.08.031</a>.","ista":"Bandeira AS, Ferber A, Kwan MA. 2017. Resilience for the Littlewood–Offord problem. Advances in Mathematics. 319, 292–312.","ieee":"A. S. Bandeira, A. Ferber, and M. A. Kwan, “Resilience for the Littlewood–Offord problem,” <i>Advances in Mathematics</i>, vol. 319. Elsevier, pp. 292–312, 2017.","chicago":"Bandeira, Afonso S., Asaf Ferber, and Matthew Alan Kwan. “Resilience for the Littlewood–Offord Problem.” <i>Advances in Mathematics</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.aim.2017.08.031\">https://doi.org/10.1016/j.aim.2017.08.031</a>."},"arxiv":1,"external_id":{"arxiv":["1609.08136"]},"title":"Resilience for the Littlewood–Offord problem","publication":"Advances in Mathematics","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1609.08136"}],"type":"journal_article","publisher":"Elsevier","year":"2017","language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2017.08.031","date_published":"2017-10-15T00:00:00Z","oa":1,"_id":"9588","author":[{"first_name":"Afonso S.","full_name":"Bandeira, Afonso S.","last_name":"Bandeira"},{"last_name":"Ferber","full_name":"Ferber, Asaf","first_name":"Asaf"},{"first_name":"Matthew Alan","full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","orcid":"0000-0002-4003-7567"}],"intvolume":"       319","article_processing_charge":"No","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","extern":"1","date_created":"2021-06-22T11:51:27Z","article_type":"original","volume":319,"quality_controlled":"1","publication_identifier":{"issn":["0001-8708"]},"month":"10"},{"month":"01","publication_identifier":{"issn":["0001-8708"]},"quality_controlled":"1","publication":"Advances in Mathematics","title":"How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency","article_type":"original","volume":208,"date_created":"2020-09-18T10:48:27Z","citation":{"chicago":"Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms Have Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic Tangency.” <i>Advances in Mathematics</i>. Elsevier, 2007. <a href=\"https://doi.org/10.1016/j.aim.2006.03.012\">https://doi.org/10.1016/j.aim.2006.03.012</a>.","ieee":"A. Gorodetski and V. Kaloshin, “How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency,” <i>Advances in Mathematics</i>, vol. 208, no. 2. Elsevier, pp. 710–797, 2007.","mla":"Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms Have Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic Tangency.” <i>Advances in Mathematics</i>, vol. 208, no. 2, Elsevier, 2007, pp. 710–97, doi:<a href=\"https://doi.org/10.1016/j.aim.2006.03.012\">10.1016/j.aim.2006.03.012</a>.","short":"A. Gorodetski, V. Kaloshin, Advances in Mathematics 208 (2007) 710–797.","ista":"Gorodetski A, Kaloshin V. 2007. How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency. Advances in Mathematics. 208(2), 710–797.","apa":"Gorodetski, A., &#38; Kaloshin, V. (2007). How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2006.03.012\">https://doi.org/10.1016/j.aim.2006.03.012</a>","ama":"Gorodetski A, Kaloshin V. How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency. <i>Advances in Mathematics</i>. 2007;208(2):710-797. doi:<a href=\"https://doi.org/10.1016/j.aim.2006.03.012\">10.1016/j.aim.2006.03.012</a>"},"issue":"2","extern":"1","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       208","keyword":["General Mathematics"],"author":[{"full_name":"Gorodetski, A.","first_name":"A.","last_name":"Gorodetski"},{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","first_name":"Vadim"}],"_id":"8511","day":"30","publication_status":"published","date_published":"2007-01-30T00:00:00Z","oa_version":"None","page":"710-797","abstract":[{"text":"Here we study an amazing phenomenon discovered by Newhouse [S. Newhouse, Non-density of Axiom A(a) on S2, in: Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., 1970, pp. 191–202; S. Newhouse,\r\nDiffeomorphisms with infinitely many sinks, Topology 13 (1974) 9–18; S. Newhouse, The abundance of\r\nwild hyperbolic sets and nonsmooth stable sets of diffeomorphisms, Publ. Math. Inst. Hautes Études Sci.\r\n50 (1979) 101–151]. It turns out that in the space of Cr smooth diffeomorphisms Diffr(M) of a compact\r\nsurface M there is an open set U such that a Baire generic diffeomorphism f ∈ U has infinitely many coexisting sinks. In this paper we make a step towards understanding “how often does a surface diffeomorphism\r\nhave infinitely many sinks.” Our main result roughly says that with probability one for any positive D a\r\nsurface diffeomorphism has only finitely many localized sinks either of cyclicity bounded by D or those\r\nwhose period is relatively large compared to its cyclicity. It verifies a particular case of Palis’ Conjecture\r\nsaying that even though diffeomorphisms with infinitely many coexisting sinks are Baire generic, they have\r\nprobability zero.\r\nOne of the key points of the proof is an application of Newton Interpolation Polynomials to study the dynamics initiated in [V. Kaloshin, B. Hunt, A stretched exponential bound on the rate of growth of the number\r\nof periodic points for prevalent diffeomorphisms I, Ann. of Math., in press, 92 pp.; V. Kaloshin, A stretched\r\nexponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II,\r\npreprint, 85 pp.].","lang":"eng"}],"doi":"10.1016/j.aim.2006.03.012","language":[{"iso":"eng"}],"year":"2007","publisher":"Elsevier","date_updated":"2021-01-12T08:19:47Z","status":"public","type":"journal_article"}]