SRB attractors with intermingled basins for non-hyperbolic diffeomorphisms

Abstract

We investigate a class of non-hyperbolic diffeomorphisms defined onthe product space. By using the Pesin theory combined with thegeneral theory of differentiable dynamical systems, we prove thatthere are exactly two SRB attractors, and their basins cover a fullmeasure subset of the ambient manifold. Furthermore, we prove that the basins ofSRB attractors have the strange intermingled phenomenon, i.e. theyare measure-theoretically dense in each other. The intermingledphenomena have been observed in many physical systems by numericalexperiments, and considered to be important to some fundamentalproblems in physical, biology and computer science etc. Finally, wedescribe a concrete example for application.