[{"title":"Generic diffeomorphisms with superexponential growth of number of periodic orbits","day":"01","intvolume":" 211","doi":"10.1007/s002200050811","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"}],"date_published":"2000-04-01T00:00:00Z","publication_identifier":{"issn":["0010-3616","1432-0916"]},"_id":"8525","oa_version":"None","extern":"1","page":"253-271","date_updated":"2021-01-12T08:19:52Z","citation":{"ama":"Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. *Communications in Mathematical Physics*. 2000;211:253-271. doi:10.1007/s002200050811","chicago":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” *Communications in Mathematical Physics*. Springer Nature, 2000. https://doi.org/10.1007/s002200050811.","mla":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” *Communications in Mathematical Physics*, vol. 211, Springer Nature, 2000, pp. 253–71, doi:10.1007/s002200050811.","ista":"Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.","ieee":"V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” *Communications in Mathematical Physics*, vol. 211. Springer Nature, pp. 253–271, 2000.","apa":"Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of number of periodic orbits. *Communications in Mathematical Physics*. Springer Nature. https://doi.org/10.1007/s002200050811","short":"V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271."},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","year":"2000","publication_status":"published","publication":"Communications in Mathematical Physics","publisher":"Springer Nature","article_processing_charge":"No","type":"journal_article","month":"04","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"quality_controlled":"1","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","first_name":"Vadim","orcid":"0000-0002-6051-2628"}],"article_type":"original","volume":211,"date_created":"2020-09-18T10:50:20Z"}]