An extension of the Artin-Mazur theorem
| dc.creator | Kaloshin, Vadim Yu. | |
| dc.date | 1999-09-01 | |
| dc.date.accessioned | 2026-07-07T05:30:59Z | |
| dc.date.available | 2026-07-07T05:30:59Z | |
| dc.description | Let M be a compact manifold. We call a mapping f in C^r(M,M) an Artin-Mazur mapping if the number of isolated periodic points of f^n grows at most exponentially in n. Artin and Mazur posed the following problem: What can be said about the set of Artin-Mazur mappings with only transversal periodic orbits? Recall that a periodic orbit of period n is called transversal if the linearization df^n at this point has for an eigenvalue no nth roots of unity. Notice that a hyperbolic periodic point is always transversal, but not vice versa. We consider not the whole space C^r(M,M) of mappings of M into itself, but only its open subset Diff^r(M). The main result of this paper is the following theorem: Let 1 <= r < \infty. Then the set of Artin-Mazur diffeomorphisms with only hyperbolic periodic orbits is dense in the space Diff^r(M). | |
| dc.description | 13 pages, published version, abstract added in migration | |
| dc.identifier | https://arxiv.org/abs/math/9909196 | |
| dc.identifier | http://arxiv.org/abs/math/9909196 | |
| dc.identifier | Ann. of Math. (2) 150 (1999), no. 2, 729-741 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79183 | |
| dc.subject | Dynamical Systems | |
| dc.title | An extension of the Artin-Mazur theorem | |
| dc.type | text |