[{"volume":211,"extern":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:19:52Z","citation":{"chicago":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2000. <a href=\"https://doi.org/10.1007/s002200050811\">https://doi.org/10.1007/s002200050811</a>.","ieee":"V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” <i>Communications in Mathematical Physics</i>, vol. 211. Springer Nature, pp. 253–271, 2000.","ama":"Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. <i>Communications in Mathematical Physics</i>. 2000;211:253-271. doi:<a href=\"https://doi.org/10.1007/s002200050811\">10.1007/s002200050811</a>","apa":"Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of number of periodic orbits. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s002200050811\">https://doi.org/10.1007/s002200050811</a>","ista":"Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.","mla":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>, vol. 211, Springer Nature, 2000, pp. 253–71, doi:<a href=\"https://doi.org/10.1007/s002200050811\">10.1007/s002200050811</a>.","short":"V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271."},"year":"2000","date_published":"2000-04-01T00:00:00Z","type":"journal_article","doi":"10.1007/s002200050811","publication_identifier":{"issn":["0010-3616","1432-0916"]},"day":"01","abstract":[{"text":"Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented.","lang":"eng"}],"page":"253-271","quality_controlled":"1","language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"publisher":"Springer Nature","article_type":"original","publication":"Communications in Mathematical Physics","_id":"8525","author":[{"first_name":"Vadim","last_name":"Kaloshin","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"publication_status":"published","oa_version":"None","date_created":"2020-09-18T10:50:20Z","article_processing_charge":"No","month":"04","title":"Generic diffeomorphisms with superexponential growth of number of periodic orbits","intvolume":"       211"},{"publication":"Communications in Mathematical Physics","oa_version":"None","month":"10","language":[{"iso":"eng"}],"type":"journal_article","date_published":"1997-10-01T00:00:00Z","publication_identifier":{"issn":["0010-3616"]},"publist_id":"4164","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","scopus_import":"1","_id":"2729","issue":"3","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan"}],"article_processing_charge":"No","date_created":"2018-12-11T11:59:18Z","publication_status":"published","intvolume":"       188","title":"Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates","quality_controlled":"1","page":"599 - 656","publisher":"Springer","article_type":"original","citation":{"ista":"Erdös L, Solovej J. 1997. Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates. Communications in Mathematical Physics. 188(3), 599–656.","short":"L. Erdös, J. Solovej, Communications in Mathematical Physics 188 (1997) 599–656.","mla":"Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Non-Homogeneous Magnetic Fields, II. Leading Order Asymptotic Estimates.” <i>Communications in Mathematical Physics</i>, vol. 188, no. 3, Springer, 1997, pp. 599–656, doi:<a href=\"https://doi.org/10.1007/s002200050181\">10.1007/s002200050181</a>.","ieee":"L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates,” <i>Communications in Mathematical Physics</i>, vol. 188, no. 3. Springer, pp. 599–656, 1997.","chicago":"Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Non-Homogeneous Magnetic Fields, II. Leading Order Asymptotic Estimates.” <i>Communications in Mathematical Physics</i>. Springer, 1997. <a href=\"https://doi.org/10.1007/s002200050181\">https://doi.org/10.1007/s002200050181</a>.","ama":"Erdös L, Solovej J. Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates. <i>Communications in Mathematical Physics</i>. 1997;188(3):599-656. doi:<a href=\"https://doi.org/10.1007/s002200050181\">10.1007/s002200050181</a>","apa":"Erdös, L., &#38; Solovej, J. (1997). Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s002200050181\">https://doi.org/10.1007/s002200050181</a>"},"year":"1997","date_updated":"2022-08-22T09:25:09Z","day":"01","doi":"10.1007/s002200050181","abstract":[{"lang":"eng","text":"We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous magnetic field. As in [LSY-II] for homogeneous field, this result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained in our companion paper [ES-I]."}],"acknowledgement":"L. E. gratefully acknowledges financial support from the Forschungsinstitut fur Mathematik, ETH, Zurich, where this work was started. He is also grateful for the hospitality and support of Aarhus University during his visits. The authors wish to thank the referee for the careful reading of the manuscript and the many helpful remarks and suggestions.","volume":188,"extern":"1"},{"main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02099152"}],"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_identifier":{"issn":["0010-3616"]},"publist_id":"4168","type":"journal_article","date_published":"1995-06-01T00:00:00Z","language":[{"iso":"eng"}],"oa_version":"None","month":"06","publication":"Communications in Mathematical Physics","volume":170,"extern":"1","day":"01","doi":"10.1007/BF02099152","abstract":[{"text":"We study the generalizations of the well-known Lieb-Thirring inequality for the magnetic Schrödinger operator with nonconstant magnetic field. Our main result is the naturally expected magnetic Lieb-Thirring estimate on the moments of the negative eigenvalues for a certain class of magnetic fields (including even some unbounded ones). We develop a localization technique in path space of the stochastic Feynman-Kac representation of the heat kernel which effectively estimates the oscillatory effect due to the magnetic phase factor.","lang":"eng"}],"year":"1995","citation":{"ama":"Erdös L. Magnetic Lieb-Thirring inequalities. <i>Communications in Mathematical Physics</i>. 1995;170(3):629-668. doi:<a href=\"https://doi.org/10.1007/BF02099152\">10.1007/BF02099152</a>","apa":"Erdös, L. (1995). Magnetic Lieb-Thirring inequalities. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/BF02099152\">https://doi.org/10.1007/BF02099152</a>","chicago":"Erdös, László. “Magnetic Lieb-Thirring Inequalities.” <i>Communications in Mathematical Physics</i>. Springer, 1995. <a href=\"https://doi.org/10.1007/BF02099152\">https://doi.org/10.1007/BF02099152</a>.","ieee":"L. Erdös, “Magnetic Lieb-Thirring inequalities,” <i>Communications in Mathematical Physics</i>, vol. 170, no. 3. Springer, pp. 629–668, 1995.","short":"L. Erdös, Communications in Mathematical Physics 170 (1995) 629–668.","mla":"Erdös, László. “Magnetic Lieb-Thirring Inequalities.” <i>Communications in Mathematical Physics</i>, vol. 170, no. 3, Springer, 1995, pp. 629–68, doi:<a href=\"https://doi.org/10.1007/BF02099152\">10.1007/BF02099152</a>.","ista":"Erdös L. 1995. Magnetic Lieb-Thirring inequalities. Communications in Mathematical Physics. 170(3), 629–668."},"date_updated":"2022-06-28T09:19:36Z","publisher":"Springer","article_type":"original","quality_controlled":"1","page":"629 - 668","date_created":"2018-12-11T11:59:16Z","article_processing_charge":"No","publication_status":"published","intvolume":"       170","title":"Magnetic Lieb-Thirring inequalities","_id":"2724","issue":"3","author":[{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}]},{"language":[{"iso":"eng"}],"month":"01","oa_version":"Published Version","publication":"Communications in Mathematical Physics","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"open_access":"1","url":"https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-143/issue-3/Central-limit-theorems-for-the-one-dimensional-Rayleigh-gas-with/cmp/1104249076.full"}],"publist_id":"4170","oa":1,"publication_identifier":{"issn":["0010-3616"]},"type":"journal_article","date_published":"1992-01-01T00:00:00Z","article_type":"original","publisher":"Springer","quality_controlled":"1","page":"451 - 466","intvolume":"       143","title":"Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers","date_created":"2018-12-11T11:59:15Z","article_processing_charge":"No","publication_status":"published","issue":"3","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"full_name":"Tuyen, Dao","first_name":"Dao","last_name":"Tuyen"}],"scopus_import":"1","_id":"2722","extern":"1","volume":143,"acknowledgement":"The authors are very grateful to D. Szasz and A. Kramli for valuable discussions and their encouragement. We are also indebted to D. Dϋrr for his comments and suggestions.\r\n","abstract":[{"lang":"eng","text":"A version of the one-dimensional Rayleigh gas is considered: a point particle of mass M (molecule), confined to the unit interval [0,1], is surrounded by an infinite ideal gas of point particles of mass 1 (atoms). The molecule interacts with the atoms and with the walls via elastic collision. Central limit theorems are proved for a wide class of additive functionals of this system (e.g. the number of collisions with the walls and the total length of the molecular path)."}],"day":"01","doi":"10.1007/BF02099260","year":"1992","citation":{"ama":"Erdös L, Tuyen D. Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers. <i>Communications in Mathematical Physics</i>. 1992;143(3):451-466. doi:<a href=\"https://doi.org/10.1007/BF02099260\">10.1007/BF02099260</a>","apa":"Erdös, L., &#38; Tuyen, D. (1992). Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/BF02099260\">https://doi.org/10.1007/BF02099260</a>","ieee":"L. Erdös and D. Tuyen, “Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers,” <i>Communications in Mathematical Physics</i>, vol. 143, no. 3. Springer, pp. 451–466, 1992.","chicago":"Erdös, László, and Dao Tuyen. “Central Limit Theorems for the One-Dimensional Rayleigh Gas with Semipermeable Barriers.” <i>Communications in Mathematical Physics</i>. Springer, 1992. <a href=\"https://doi.org/10.1007/BF02099260\">https://doi.org/10.1007/BF02099260</a>.","short":"L. Erdös, D. Tuyen, Communications in Mathematical Physics 143 (1992) 451–466.","mla":"Erdös, László, and Dao Tuyen. “Central Limit Theorems for the One-Dimensional Rayleigh Gas with Semipermeable Barriers.” <i>Communications in Mathematical Physics</i>, vol. 143, no. 3, Springer, 1992, pp. 451–66, doi:<a href=\"https://doi.org/10.1007/BF02099260\">10.1007/BF02099260</a>.","ista":"Erdös L, Tuyen D. 1992. Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers. Communications in Mathematical Physics. 143(3), 451–466."},"date_updated":"2022-03-16T14:24:12Z"}]