论文标题
平均共形动力系统的特殊集
Exceptional sets for average conformal dynamical systems
论文作者
论文摘要
令$ f：m \ to m $为$ c^{1+α} $ map/diffeemorlist of compact riemannian歧管$ m $和$μ$是$ m $ $ m $的扩展/双曲线$ f $ f $ f $ f $ f $ invariant borel borel概率。假设$ f $是支撑套装$ w $ $ $ $ $ w $ $ w $ $ w $ $ w $的平均形状扩展/双曲线，而$ w $是本地最大的。对于具有小熵或尺寸的任何子集$ a \子集W $，我们研究了$ a $ a $ a的拓扑熵和hausdorff尺寸，以及限制$ a $ a $ a-exceftional set。
Let $f: M \to M$ be a $C^{1+α}$ map/diffeomorphism of a compact Riemannian manifold $M$ and $μ$ be an expanding/hyperbolic ergodic $f$-invariant Borel probability measure on $M$. Assume $f$ is average conformal expanding/hyperbolic on the support set $W$ of $μ$ and $W$ is locally maximal. For any subset $A\subset W$ with small entropy or dimension, we investigate the topological entropy and Hausdorff dimensions of the $A$-exceptional set and the limit $A$-exceptional set.
