Topology Proceedings 28 No. 2 (2004), pp. 587-593

Topological entropy of monotone maps and confluent maps on regular curves

Hisao Kato

G.T. Seidler proved that the topological entropy of every homeomorphism on a regular curve is zero. L.S. Efremova and E.N. Markhrova proved that the topological entropy of every monotone map on a dendrite which satisfies some special condition is zero. N. Chinen proved that the topological entropy of every monotone map on any dendrite is zero. In this paper, we generalize these results. In fact, we investigate the topological entropy of confluent maps on regular curves. As a corollary, we show that the topological entropy of every monotone map on any regular curve is zero.

Mathematics Subject Classification: 54C70 54F20 54H20 (37E25 37B40)

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Topology Proceedings, Volume 28, No. 2 (2004)
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