n—方体上的三角形映射的拓扑熵及分歧

Topological Entropy and a Direct Bifurcation of Triangular Maps of the n-Cube

本文给出了ｎ－方体上的三角形映射的拓扑熵的下确界，证明了存在ｎ－方体上的一个具有无穷拓扑熵的２∞型映射，此外，还构造了ｎ－方体上的一个单参数的三角形映射的Ｃｏ－族，它具有如下性质，随着其参数的单调变化，映射族无穷多次地经历了从混沌到有序又返回到混沌并最终返回到有序的动力学过程．

In this paper, a lower bound of topological entropy of a triangular map of the n-cube is given. Two examples of such maps are given, which show that this lower bound is the best possible. We alsoshow that there is a triangular map of the n-cube of type 2∞ with infinite topological entropy. The abovetwc results improve and generalize the two theorems proven in [6] by Alseda et al. Moreover, a one-parameter C0-family of triangular maps of the n-cube is constructed, which has a direct bifurcation from orderto chaos or from chaos to order infinitely many times and backs to order at the end.