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Entropy Estimate for Maps on Forests | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 8، دوره 21، شماره 1، خرداد 2010 اصل مقاله (417.68 K) | ||
| نویسنده | ||
| M. Sabbaghan | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Entropy؛ Forest؛ Graph؛ Horseshoe | ||
| عنوان مقاله [English] | ||
| Entropy Estimate for Maps on Forests | ||
| نویسندگان [English] | ||
| M. Sabbaghan | ||
| چکیده [English] | ||
| 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. | ||
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