鲁棒熵膨胀性意味着一般支配
Robust entropy expansiveness implies generic domination
摘要：
令$f: M \to M$是定义在紧致无边界$d$维流形$M$，$d\geq 2$上的$C^r$-同形映射$r\geq 1$，令$H(p)$是与双曲周期点$p$相关联的同宿类.我们证明，如果存在一个$C^1$邻域$\mathcal{U}$的$f$，使每个$g\in {\mathcal U}$的延续$H(p_g)$的$H(p)$是熵膨胀的，然后有一个$Df$不变占主导地位的分裂$H(p)$的形式$E\oplus F_1\oplus... \oplus F_c\oplus G$其中$E$是收缩，$G$是扩大和所有的$F_j$是一维的，而不是双曲的。
英文摘要：
Let $f: M \to M$ be a $C^r$-diffeomorphism, $r\geq 1$, defined on a compact boundaryless $d$-dimensional manifold $M$, $d\geq 2$, and let $H(p)$ be the homoclinic class associated to the hyperbolic periodic point $p$. We prove that if there exists a $C^1$ neighborhood $\mathcal{U}$ of $f$ such that for every $g\in {\mathcal U}$ the continuation $H(p_g)$ of $H(p)$ is entropy-expansive then there is a $Df$-invariant dominated splitting for $H(p)$ of the form $E\oplus F_1\oplus... \oplus F_c\oplus G$ where $E$ is contracting, $G$ is expanding and all $F_j$ are one dimensional and not hyperbolic.
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