On topological sequence entropy and chaotic maps on inverse limit spaces
The aim of this paper is to prove the following results: a continuous map f : [0; 1] ! [0; 1] is chaotic if the shift map of : lim ([0; 1]; f) ! lim ([0; 1]; f) is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. f : lim ([0; 1]; f) ! lim ([0; 1]; f) is chaotic i...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1999 |
| País: | España |
| Institución: | Universidad Politécnica de Cartagena(UPCT) |
| Repositorio: | Repositorio Digital UPCT |
| OAI Identifier: | oai:repositorio.upct.es:10317/1026 |
| Acceso en línea: | http://hdl.handle.net/10317/1026 |
| Access Level: | acceso abierto |
| Palabra clave: | Secuencia de Entropía topológica Mapa caótico Entropía topológica Caos Topological sequence entropy Chaotic maps Chaos Topological Entropy Matemática Aplicada |
| Sumario: | The aim of this paper is to prove the following results: a continuous map f : [0; 1] ! [0; 1] is chaotic if the shift map of : lim ([0; 1]; f) ! lim ([0; 1]; f) is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. f : lim ([0; 1]; f) ! lim ([0; 1]; f) is chaotic i there exists an increasing sequence of positive integers A such that the topological sequence entropy hA( f ) > 0. Finally, for any A there exists a chaotic continuous map fA : [0; 1] ! [0; 1] such that hA( fA) = 0: |
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