Entropy Estimate for Maps on Forests

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 )≥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(rightarrow)f be a continuous function. by using the adjacency matrix of a graph, we give a lower bound for the topological entropy of f.