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Zero-entropy invariant measures for skew product diffeomorphisms

  • PENG SUN (a1)


In this paper, we study some skew product diffeomorphisms with non-uniformly hyperbolic structure along fibers and show that there is an invariant measure with zero entropy which has atomic conditional measures along fibers. For such diffeomorphisms, our result gives an affirmative answer to the question posed by Herman as to whether a smooth diffeomorphism of positive topological entropy would fail to be uniquely ergodic. The proof is based on some techniques that are analogous to those developed by Pesin and Katok, together with an investigation of certain combinatorial properties of the projected return map on the base.



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Zero-entropy invariant measures for skew product diffeomorphisms

  • PENG SUN (a1)


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