Generic diffeomorphisms with superexponential growth of number of periodic orbits

Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.

Download
No fulltext has been uploaded. References only!

Journal Article | Published | English
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.
Publishing Year
Date Published
2000-04-01
Journal Title
Communications in Mathematical Physics
Volume
211
Page
253-271
IST-REx-ID

Cite this

Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 2000;211:253-271. doi:10.1007/s002200050811
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
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.
V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” Communications in Mathematical Physics, vol. 211. Springer Nature, pp. 253–271, 2000.
Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.
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.

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar