Hyperbolic saddle measures and laminarity for holomorphic endomorphisms of $P^2C$

光滑鞍形曲面自同态的最大熵测度的有限性

Finiteness of measures of maximal entropy for smooth saddle surface endomorphisms

本文针对拓扑熵大于度的对数的闭曲面$\mathcal{C}^{\infty}$局部微分同胚，通过构造具马尔可夫性的几何矩形族、结合Yomdin理论分析不稳定曲线迭代行为，证明这类映射的最大熵遍历测度数目有限。

Structure of Julia sets for post-critically finite endomorphisms on $\mathbb{p}^2$

Let $f$ be a post-critically finite endomorphism (PCF map for short) on $\mathbb{P}^2$, let $J_1$ denote the Julia set and let $J_2$ denote the support of the measure of maximal entropy. In this paper we show that: 1. $J_1\setminus J_2$ is contained in the union of the (finitely many) basins of critical component cycles and stable manifolds of sporadic super-saddle cycles. 2. For every $x\in J_2$ which is not contained in the stable manifold of a sporadic super-saddle cycle, there is no Fatou disk containing $x$. Here sporadic means that the super-saddle cycle is not contained in a critical co…

SRB measures and homoclinic relation for Endomorphisms

In this paper we give an upper bound for the number of SRB measures of saddle type of local diffeomorphisms of boundaryless manifolds in terms of maximal cardinality of set of periodic points without any homoclinic relation.

Sur la construction de mesures selles

We build saddle measures (in a weak sense) for holomorphic endomorphisms of CP^2.