برآورد آنتروپی برای نگاشت های روی جنگل ها

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?F be a continuous function. By using the adjacency matrix of a graph, we give a lower bound for the topological entropy of f.