Smooth triangular maps of the square with closed set of periodic points

[摘要] Let (f, I) and (g(x), I) be dynamical systems defined by smooth maps f is an element of C-1 (I, I) and g(x) is an element of C-1 (I, I) of the unit interval I = [0, 1]. We consider the triangular map F(x, y) = (f(x), g(x)(y)) and prove that if every periodic point off is hyperbolic and the periodic points of F form a closed set, then every nonwandering point of F is periodic. (C) 1995 Academic Press, Inc.

[发布日期] 1995-12-15