--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Vadim foaf_name: Kaloshin, Vadim foaf_surname: Kaloshin foaf_workInfoHomepage: http://www.librecat.org/personId=FE553552-CDE8-11E9-B324-C0EBE5697425 orcid: 0000-0002-6051-2628 bibo_doi: 10.1007/s002200050811 bibo_volume: 211 dct_date: 2000^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0010-3616 - http://id.crossref.org/issn/1432-0916 dct_language: eng dct_publisher: Springer Nature@ dct_subject: - Mathematical Physics - Statistical and Nonlinear Physics dct_title: Generic diffeomorphisms with superexponential growth of number of periodic orbits@ ...