Some remarks on chaos in topological dynamics

Wang, Huoyung ^[1] ; Fu, Heman ^[2]
1. [1] Guangzhou University
  
  Guangzhou University
  
  China
2. [2] Zhaoqing University
  
  Zhaoqing University
  
  China
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 12, Nº. 2, 2011, págs. 95-100
Idioma: inglés
Enlaces
- Texto completo
Resumen
- Bau-Sen Du introduced a notion of chaos which is stronger than Li-Yorke sensitivity. A TDS (X, f) is called chaotic if there is a positive e such that for any x and any nonempty open set V of X there is a point y in V such that the pair (x, y) is proximal but not e-asymptotic. In this article, we show that a TDS (T, f) is transitive but not mixing if and only if (T, f) is Li-Yorke sensitive but not chaotic, where T is a tree. Moreover, we compare such chaos with other notions of chaos.