{"language":[{"iso":"eng"}],"year":"2016","volume":348,"publication_identifier":{"issn":["0010-3616","1432-0916"]},"title":"A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems","intvolume":"       348","date_updated":"2021-01-12T08:19:39Z","date_created":"2020-09-18T10:45:50Z","month":"11","citation":{"mla":"Guardia, M., et al. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” <i>Communications in Mathematical Physics</i>, vol. 348, Springer Nature, 2016, pp. 321–61, doi:<a href=\"https://doi.org/10.1007/s00220-016-2705-9\">10.1007/s00220-016-2705-9</a>.","ista":"Guardia M, Kaloshin V, Zhang J. 2016. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. 348, 321–361.","short":"M. Guardia, V. Kaloshin, J. Zhang, Communications in Mathematical Physics 348 (2016) 321–361.","chicago":"Guardia, M., Vadim Kaloshin, and J. Zhang. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2016. <a href=\"https://doi.org/10.1007/s00220-016-2705-9\">https://doi.org/10.1007/s00220-016-2705-9</a>.","ieee":"M. Guardia, V. Kaloshin, and J. Zhang, “A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems,” <i>Communications in Mathematical Physics</i>, vol. 348. Springer Nature, pp. 321–361, 2016.","ama":"Guardia M, Kaloshin V, Zhang J. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. <i>Communications in Mathematical Physics</i>. 2016;348:321-361. doi:<a href=\"https://doi.org/10.1007/s00220-016-2705-9\">10.1007/s00220-016-2705-9</a>","apa":"Guardia, M., Kaloshin, V., &#38; Zhang, J. (2016). A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-016-2705-9\">https://doi.org/10.1007/s00220-016-2705-9</a>"},"article_processing_charge":"No","doi":"10.1007/s00220-016-2705-9","date_published":"2016-11-01T00:00:00Z","publication_status":"published","quality_controlled":"1","oa_version":"None","article_type":"original","_id":"8493","status":"public","abstract":[{"lang":"eng","text":"In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior."}],"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","publisher":"Springer Nature","author":[{"full_name":"Guardia, M.","last_name":"Guardia","first_name":"M."},{"orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","first_name":"Vadim"},{"last_name":"Zhang","full_name":"Zhang, J.","first_name":"J."}],"publication":"Communications in Mathematical Physics","day":"01","page":"321-361"}