Some remarks on chaos in topological dynamics | Zendy

Huoyung Wang | Zendy; Heman Fu | Zendy

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Some remarks on chaos in topological dynamics

Author(s) -

Huoyung Wang,

Heman Fu

Publication year - 2013

Publication title -

applied general topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.638

H-Index - 13

eISSN - 1989-4147

pISSN - 1576-9402

DOI - 10.4995/agt.2011.1645

Subject(s) - mathematics , chaos (operating system) , transitive relation , chaotic , mixing (physics) , tree (set theory) , pure mathematics , topological dynamics , set (abstract data type) , combinatorics , discrete mathematics , physics , computer science , quantum mechanics , artificial intelligence , biochemistry , chemistry , topological tensor product , computer security , functional analysis , gene , programming language

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

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