University of TehranJournal of Sciences, Islamic Republic of Iran1016-110421120100301Entropy Estimate for Maps on ForestsEntropy Estimate for Maps on Forests20140ENM.SabbaghanJournal Article19700101A 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 ) ? 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.https://jsciences.ut.ac.ir/article_20140_e38aa3190e3785f59e2a798f507b09a0.pdf