The Weakly Chain Transitive Maps

Abstract:

Let (X,f) be a compact system. In this note we prove that if f satisfies Lipschitz condition, then f is totally weakly chain transitive if and only if f is weakly chain transitive by introducing the notion of the weak chain transitivity and the totally weak chain transitivity. The note also proves that the set-valued map of f is weakly chain transitive implies f is weakly chain transitive.

• Periodical: Advanced Materials Research (Volumes 834-836)
• Pages: 1836-1839
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.834-836.1836
• Online since: October 2013
• Authors: Xin Meng
• Keywords: Set-Valued Map, Totally Weakly Chain Transitivity, Weak Chain Transitivity

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