光滑斜积的最大相对熵测度的基数
On the cardinality of measures of maximal relative entropy for smooth skew products
AI总结：
本文针对传递Anosov基上的$\mathcal C^{1+\alpha}$光滑斜积微分同胚，证明其最大相对熵遍历双曲测度至多可数，且二维纤维情形下正相对拓扑熵时该类遍历测度也至多可数。
摘要：
设$\Omega$和$M$为紧光滑流形，$\Theta:\Omega\times M\to\Omega\times M$是定义在传递Anosov基上的$\mathcal C^{1+\alpha}$斜积微分同胚。本文证明$\Theta$至多存在可数个具有最大相对熵的遍历双曲测度；当$\dim M=2$时，若$\Theta$的相对拓扑熵为正，则其至多存在可数个具有最大相对熵的遍历测度。
英文摘要：
Let $Ω$ and $M$ be compact smooth manifolds and let $Θ:Ω\times M\toΩ\times M$ be a $\mathcal C^{1+α}$ skew-product diffeomorphism over a transitive Anosov base. We show that $Θ$ has at most countably many ergodic hyperbolic measures of maximal relative entropy. When $\dim M=2$, if $Θ$ has positive relative topological entropy, then $Θ$ has at most countably many ergodic measures of maximal relative entropy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
