Physical measures for certain partially hyperbolic attractors on 3-manifolds
Physical measures for certain partially hyperbolic attractors on 3-manifolds
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3-流形上某些部分双曲吸引子的物理测量
DOI：
10.1017/etds.2017.24
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发表时间：
2015
影响因子：
0.9
通讯作者：
Ricardo Bortolotti
中科院分区：
文献类型：
--
作者：
Ricardo Bortolotti
本文分析了一类中心方向具有中性性质的部分双曲吸引子的遍历性质；其主要特征是不稳定叶的凸出之间具有横向性，通过稳定叶理凸出。我们证明了满足横向性、中心方向中立性和稳定叶理的规则性条件的部分双曲吸引子承认有限数量的物理测度，符合遍历u-Gibbs态，其盆地的结合具有充分的勒贝格测度。此外，我们还描述了满足这些性质的鲁棒非双曲吸引子的构造。
In this work, we analyze ergodic properties of certain partially hyperbolic attractors whose central direction has a neutral behavior; the main feature is a condition of transversality between the projections of unstable leaves, projecting through the stable foliation. We prove that partial hyperbolic attractors satisfying this condition of transversality, neutrality in the central direction and regularity of the stable foliation admit a finite number of physical measures, coinciding with the ergodic u-Gibbs States, whose union of the basins has full Lebesgue measure. Moreover, we describe the construction of robustly non-hyperbolic attractors satisfying these properties.