A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms
| dc.creator | Kaloshin, Vadim Yu. | |
| dc.creator | Hunt, Brian | |
| dc.date | 2000-12-21 | |
| dc.date.accessioned | 2026-07-07T04:39:23Z | |
| dc.date.available | 2026-07-07T04:39:23Z | |
| dc.description | Let M be a compact manifold of dimension at least 2, Diff^r(M) be the space of C^r diffeomorphisms of M. Define for any diffeomorphism f in Diff^r(M) number of isolated periodic points of period n by P_n(f)=# {isolated x in M: f^n(x)=x}. Artin--Mazur proved that for a dense set of diffeomorphisms the number of periodic points P_n(f) growth at most exponentially fast in n. The author proved that there is an open set N \subset Diff^r(M) such that for a Baire generic set of diffeomorphisms the number of periodic points P_n(f) growth arbitrarily fast. Arnold posed a problem: Prove that diffeomorphisms with at most exponential growth of the number of periodic points in period have probability one. In this paper we annonce and exhibit key ingredients for a partial solution to Arnold's problem: we prove that for any epsilon>0 with probability one the number of periodic points is bounded by a streched exponential estimate P_n(f)<exp(Cn^{1+epsilon}). | |
| dc.description | 19 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0012224 | |
| dc.identifier | http://arxiv.org/abs/math/0012224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60638 | |
| dc.subject | Dynamical Systems | |
| dc.title | A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms | |
| dc.type | text |