[{"date_created":"2020-09-18T10:50:20Z","day":"01","dini_type":"doc-type:article","quality_controlled":"1","language":[{}],"article_processing_charge":"No","uri_base":"https://research-explorer.ista.ac.at","volume":211,"page":"253-271","intvolume":" 211","month":"04","oa_version":"None","publication":"Communications in Mathematical Physics","extern":"1","type":"journal_article","status":"public","date_updated":"2021-01-12T08:19:52Z","abstract":[{"lang":"eng"}],"publication_identifier":{"issn":[]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.","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","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.","short":"V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.","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.","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."},"creator":{"login":"dernst","id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},"author":[{"last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"dc":{"creator":["Kaloshin, Vadim"],"source":["Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. *Communications in Mathematical Physics*. 2000;211:253-271. doi:10.1007/s002200050811"],"description":["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."],"language":["eng"],"publisher":["Springer Nature"],"rights":["info:eu-repo/semantics/closedAccess"],"title":["Generic diffeomorphisms with superexponential growth of number of periodic orbits"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1007/s002200050811","info:eu-repo/semantics/altIdentifier/issn/0010-3616","info:eu-repo/semantics/altIdentifier/issn/1432-0916"],"subject":["Mathematical Physics","Statistical and Nonlinear Physics"],"date":["2000"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"identifier":["https://research-explorer.ista.ac.at/record/8525"]},"keyword":[],"publication_status":"published","article_type":"original","_id":"8525","date_published":"2000-04-01T00:00:00Z"}]