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SRB attractors with intermingled basins for non-hyperbolic diffeomorphisms

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  • We investigate a class of non-hyperbolic diffeomorphisms defined on the product space. By using the Pesin theory combined with the general theory of differentiable dynamical systems, we prove that there are exactly two SRB attractors, and their basins cover a full measure subset of the ambient manifold. Furthermore, we prove that the basins of SRB attractors have the strange intermingled phenomenon, i.e. they are measure-theoretically dense in each other. The intermingled phenomena have been observed in many physical systems by numerical experiments, and considered to be important to some fundamental problems in physical, biology and computer science etc. Finally, we describe a concrete example for application.
    Mathematics Subject Classification: Primary: 37C40; Secondary: 37D25, 37D30, 37D45.

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