Commutativity and non-commutativity of the topological sequence entropy
In this paper we study the commutativity property for topological sequence entropy. We prove that if $X$ is a compact metric space and $f,g: X\rightarrow X$ are continuous maps then $h _A(f\circ g)=h_A(g\circ f)$ for every increasing sequence $A$ if $X=[0,1]$, and construct a counterexample for the...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 1999 |
| País: | España |
| Recursos: | Universidad Politécnica de Cartagena(UPCT) |
| Repositorio: | Repositorio Digital UPCT |
| OAI Identifier: | oai:repositorio.upct.es:10317/1029 |
| Acesso em linha: | http://hdl.handle.net/10317/1029 |
| Access Level: | acceso abierto |
| Palavra-chave: | Conmutatividad Secuencia de la entropía topológica Commutativity Topological sequence entropy Matemática Aplicada |
| Resumo: | In this paper we study the commutativity property for topological sequence entropy. We prove that if $X$ is a compact metric space and $f,g: X\rightarrow X$ are continuous maps then $h _A(f\circ g)=h_A(g\circ f)$ for every increasing sequence $A$ if $X=[0,1]$, and construct a counterexample for the general case. In the interim, we also show that the equality $h_A(f)=h_A(f\vert _{\cap _{n\ge 0}f^n(X)})$ is true if $X=[0,1]$ but does not necessarily hold if $X$ is an arbitrary compact metric space. |
|---|