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Paper Information

Journal:   JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN   WINTER 2010 , Volume 21 , Number 1; Page(s) 65 To 74.
 
Paper: 

ENTROPY ESTIMATE FOR MAPS ON FORESTS

 
 
Author(s):  GOLBAHARAN A., SABAGHAN M.*
 
* FACULTY OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE, UNIVERSITY COLLEGE OF SCIENCE, UNIVERSITY OF TEHRAN, TEHRAN, ISLAMIC REPUBLIC OF IRAN
 
Abstract: 

A 1993 result of J. Llibre, and M. Misiurewicz, (Theorem A [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h(f)³ logs. Also a 1980 result of L.S. Block, J. Guckenheimer, M. Misiurewicz and L.S. Young (Lemma 1.5 [3]) states that if G is an A-graph of f then h(G) £ h( f ). In this paper we generalize Theorem A and Lemma 1.5 for continuous functions on forests. Let F be a forest and f : F®F be a continuous function. By using the adjacency matrix of a graph, we give a lower bound for the topological entropy of f.

 
Keyword(s): ENTROPY, FOREST, GRAPH, HORSESHOE
 
References: 
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