In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined...In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined on a general compact metric space but not on a continuum such that it has zero topological entropy and is not topologically mixing.展开更多
基金Supported by the Foundation of the Jiangxi Education Department（GJJ11295） Sup- ported by the Natural Science Foundation of Jiangxi Province（20114BAB201006）
文摘In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined on a general compact metric space but not on a continuum such that it has zero topological entropy and is not topologically mixing.
