科研之友
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摘要
We study an interplay between homoclinic behavior and singularities in surface endomorphisms. We show that appropriate rescalings near homoclinic orbits intersecting fold singularities yield families of noninvertible Henon-like maps. Then we construct positive measure sets of parameters corresponding to maps which exhibit nonuniformly hyperbolic behavior. This implies an extension of the celebrated theorem of Benedicks and Carleson, and that of Mora and Viana to surface endomorphisms.
- 出版日期2011-6
