Nonwandering set of points of skew-product maps with base having closed set of periodic points

作者：Garcia Guirao Juan Luis; Garcia Rubio Raquel

来源：Journal of Mathematical Analysis and Applications, 2010, 362(2): 350-354.

DOI：10.1016/j.jmaa.2009.08.007

• Discrete dynamical system
• Skew-product map
• Nonwandering point

The aim of the present paper is to study the structure of the nonwandering set of points Omega(.) for the skew-product maps C(Delta)*(I(2)) of the unit square I(2) = [0, 1] x [0, 1], (x, y) -> (f (x), g(x, y)), with base f having closed set of periodic points. For every F is an element of C(Delta)* (I(2)) and every point (x, y) with x periodic of period p(x) by f and y not chain recurrent of F(px)vertical bar(Ix), where I(x) = {x} x I. we prove that (x, y) is not an element of Omega(F). On the other hand we construct a map F(0) is an element of C(Delta)* (I(2)) with an isolated fixed point x(0) of f and y(0) is not an element of Omega(F vertical bar(Ix0)) such that (x(0), y(0)) is an element of Omega (F(0)).

• 出版日期2010-2-15