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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@
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