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arXiv math/0403537math.DS
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最终体积膨胀的自同态的向后体积收缩

Backward volume contraction for endomorphisms with eventual volume expansion

Jose F. Alves, Armando Castro, Vilton Pinheiro

摘要:

考虑紧黎曼流形上的光滑映射。我们证明了在最终体积膨胀勒贝格几乎处处的一些温和的条件下,我们有一致的向后体积收缩勒贝格几乎每一个点的每一个预轨道。

英文摘要:

We consider smooth maps on compact Riemannian manifolds. We prove that under some mild condition of eventual volume expansion Lebesgue almost everywhere we have uniform backward volume contraction on every pre-orbit for Lebesgue almost every point.

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