SRB measures for partially hyperbolic systems whose central direction is mostly contracting
SRB measures for partially hyperbolic systems whose central direction is mostly contracting
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DOI：
10.1007/bf02810585
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发表时间：
2000-12
影响因子：
1
通讯作者：
C. Bonatti;M. Viana
中科院分区：
文献类型：
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作者：
C. Bonatti;M. Viana
我们考虑部分双曲同胚保持分裂的切丛成一个强不稳定的子丛Euu（一致膨胀）和一个子丛Ec，占主导地位的Euu。我们证明了如果中心方向Ec对于自同构（负李雅普诺夫指数）是大部分收缩的，则遍历Gibbs u-态是Sinai-Ruelle-Bowen测度，并且它们的盆域覆盖了一个全测度子集.如果强不稳定的叶子是密集的，则存在唯一的Sinai-Ruelle-Bowen测度。我们描述了这些结果的一些应用，我们还介绍了一个建设的鲁棒传递dieomorphisms在尺寸大于3，没有一致双曲（既不收缩也不膨胀）不变的子丛。
We consider partially hyperbolic di eomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle Euu (uniformly expanding) and a subbundle Ec, dominated by Euu. We prove that if the central direction Ec is mostly contracting for the di eomorphism (negative Lyapunov exponents), then the ergodic Gibbs u-states are the Sinai-Ruelle-Bowen measures, there are nitely many of them, and their basins cover a full measure subset. If the strong-unstable leaves are dense, there is a unique Sinai-Ruelle-Bowen measure. We describe some applications of these results, and we also introduce a construction of robustly transitive di eomorphisms in dimension larger than three, having no uniformly hyperbolic (neither contracting nor expanding) invariant subbundles.