{"publication_identifier":{"issn":["0010-3616","1432-0916"]},"author":[{"full_name":"Kaloshin, Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","first_name":"Vadim"}],"date_created":"2020-09-18T10:50:20Z","date_updated":"2021-01-12T08:19:52Z","language":[{"iso":"eng"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Generic diffeomorphisms with superexponential growth of number of periodic orbits","page":"253-271","day":"01","year":"2000","_id":"8525","doi":"10.1007/s002200050811","quality_controlled":"1","intvolume":"       211","type":"journal_article","publication_status":"published","volume":211,"extern":"1","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_type":"original","month":"04","publication":"Communications in Mathematical Physics","publisher":"Springer Nature","citation":{"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.","short":"V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.","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>.","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>","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>.","ista":"Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271."},"status":"public","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"}],"oa_version":"None","date_published":"2000-04-01T00:00:00Z"}