论文标题
维定双曲线SRB测量的差异的尺寸近似
Dimension approximation for diffeomorphisms preserving hyperbolic SRB measures
论文作者
论文摘要
对于C^{1+α}的差异形态f，保留双曲线的Ergodic SRB Measuien，Katok的显着结果断言，通过一系列多余的杂交集\ {λ_n\} _ {n \ geq1}来近似μCAN。在本文中，我们证明了不稳定的歧管上λ_n的hausdorff尺寸趋向于不稳定的歧管的维度。此外，如果稳定方向是一个维度，则通过λ_n的Hausdorff尺寸近似μCAN的Hausdorff尺寸。为了建立这些结果，我们利用了-in^{s}（\ cdot，f^n）的平衡度量的条件度量的U -GIBB属性以及均匀双曲动力学系统的性质。
For a C^{1+α} diffeomorphism f preserving a hyperbolic ergodic SRB measure μ, Katok's remarkable results assert that μcan be approximated by a sequence of hyperbolic sets \{Λ_n\}_{n\geq1}. In this paper, we prove the Hausdorff dimension for Λ_n on the unstable manifold tends to the dimension of the unstable manifold. Furthermore, if the stable direction is one dimension, then the Hausdorff dimension of μcan be approximated by the Hausdorff dimension of Λ_n. To establish these results, we utilize the u-Gibbs property of the conditional measure of the equilibrium measure of -ψ^{s}(\cdot,f^n) and the properties of the uniformly hyperbolic dynamical systems.
