Topological entropy and periods of self–maps on compact manifolds
Let (M; f) be a discrete dynamical system induced by a self{map f defined on a smooth compact connected n{dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C1, and (2) f has infinitely many...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad Politécnica de Cartagena(UPCT) |
| Repositorio: | Repositorio Digital UPCT |
| OAI Identifier: | oai:repositorio.upct.es:10317/8503 |
| Acceso en línea: | http://hdl.handle.net/10317/8503 https://www.math.uh.edu/~hjm/Vol43-4.html |
| Access Level: | acceso abierto |
| Palabra clave: | Compact manifold Topological entropy Discrete dynamical systems Lefschetz numbers Lefschetz zeta function Periodic point Matemática Aplicada 12 Matemáticas |
| Sumario: | Let (M; f) be a discrete dynamical system induced by a self{map f defined on a smooth compact connected n{dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C1, and (2) f has infinitely many periodic points when f is C1 and f(M) ⊆ Int(M). Moreover, for the particular manifolds Sn, Sn x Sm, CPn and HPn we improve the previous sufficient conditions. |
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