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