Zero Entropy Invariant Measures for Some Skew Product Diffeomorphisms
نویسنده
چکیده
In this paper we study some skew product diffeomorphisms with nonuniformly hyperbolic structure along fibers. We show that there is an invariant measure with zero entropy which has atomic conditional measures along fibers. This gives affirmative answer for these diffeomorphisms to the question suggested by Herman that a smooth diffeomorphism of positive topological entropy fails to be uniquely ergodic. The proof is based on some techniques analogous to those developed by Pesin ([10]) and Katok ([6], [8]) with investigation on some combinatorial properties of the projected return map on the base.
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تاریخ انتشار 2008