Topological entropy and special [alpha]-limit points of graph maps

Let G a graph and f : G [right arrow] G be a continuous map. Denote by h(f), R(f), and SA(/) the topological entropy, the set of recurrent points, and the set of special [alpha]-limit points of f, respectively. In this paper, we show that h(f) > 0 if and only if SA(f) - R(f) [not equal to] 0.

Saved in:
Bibliographic Details
Published in:Discrete dynamics in nature and society 2011-01, Vol.2011
Main Authors: Sun, Taixiang, Su, Guangwang, Liang, Hailan, He, Qiuli
Format: Article
Language:English
Subjects:
Analysis
Entropy
Entropy (Information theory)
Mathematics
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let G a graph and f : G [right arrow] G be a continuous map. Denote by h(f), R(f), and SA(/) the topological entropy, the set of recurrent points, and the set of special [alpha]-limit points of f, respectively. In this paper, we show that h(f) > 0 if and only if SA(f) - R(f) [not equal to] 0.
ISSN:1026-0226
1607-887X
DOI:10.1155/2011/132985