Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation
Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation
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DOI：
10.3934/jmd.2013.7.565
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发表时间：
2013-03
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影响因子：
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通讯作者：
Doris Bohnet
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文献类型：
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作者：
Doris Bohnet
考虑具有一致紧形f不变中心叶状的光滑紧形M上的部分双曲c1 -微分同构。我们证明了如果不稳定束是一维定向的，那么中心叶理的完整性处处消失，中心叶理的商空间是一个环面，f在其上诱导出双曲自同构，特别是f是中心可传递的。在不受不稳定维数、稳定维数和中心维数限制的情况下，我们得到了进一步有趣的结果：证明了商动力学链循环集的一种谱分解，建立了不稳定叶上完整不变测度族（Margulis测度）的存在性。
We consider a partially hyperbolic C1-diffeomorphism f on a smooth compact manifold M with a uniformly compact f-invariant center foliation. We show that if the unstable bundle is one-dimensional and oriented, then the holonomy of the center foliation vanishes everywhere, the quotient space of the center foliation is a torus and f induces a hyperbolic automorphism on it, in particular, f is centrally transitive. We actually obtain further interesting results without restrictions on the unstable, stable and center dimension: we prove a kind of spectral decomposition for the chain recurrent set of the quotient dynamics, and we establish the existence of a holonomy invariant family of measures on the unstable leaves (Margulis measure).