Continuity of Topological Entropy of One Dimensional Maps with Degenerate Critical Points

Abstract. One dimensional maps with degenerate critical points are studied and we give a larger class of Cr functions whose topological entropy is continuous. There are many studies of topological entropy of one dimensional maps. M. Misiurewicz and W. Szlenk [7] showed that topological entropy is lower semi-continuous for piecewise monotone C0 maps with C0 topology. More-over, if none of the critical points of a C1 map are degenerate, its entrop