论文标题
某些部分双曲系统的体积增长和拓扑熵
Volume growth and topological entropy of certain partially hyperbolic systems
论文作者
论文摘要
令$ f $为紧凑型歧管上的$ c^{1} $ diffemorthism $ m $承认部分双曲线拆分$ tm = e^{s} \ oplus _ {\ prec} e^{1} e^{1} \oplus_{\prec}E^{l}\oplus_{\prec} E^{u}$ where $E^{s}$ is uniformly contracting, $E^{u}$ is uniformly expanding and $\dim E^{i}=1,\,1\leq i\leq l.$ We prove an entropy formula W.R.T.切线束中子空间的体积增长率： $ h _ {\ rm {top}}}（f）= \ lim_ {n \ to+\ infty} \ frac {1} {n} {n} {n} \ log \ log \ int \ max_ {v \ subset t_}
Let $f$ be a $C^{1}$ diffeomorphism on a compact manifold $M$ admitting a partially hyperbolic splitting $TM=E^{s}\oplus_{\prec} E^{1}\oplus_{\prec} E^{2}\cdots \oplus_{\prec}E^{l}\oplus_{\prec} E^{u}$ where $E^{s}$ is uniformly contracting, $E^{u}$ is uniformly expanding and $\dim E^{i}=1,\,1\leq i\leq l.$ We prove an entropy formula w.r.t. the volume growth rate of subspaces in the tangent bundle: $$h_{\rm{top}}(f)=\lim_{n\to+\infty}\frac{1}{n}\log\int\max_{V\subset T_{x}M}|\det Df_{x}^{n}|_{V}|\,d x.$$
