关于Viana-Alves映射相关的拉伸指数衰减的注记

基动力学中具有奇点的类Viana映射的遍历性

Ergodic properties of Viana-like maps with singularities in the base dynamics

我们考虑两个例子的维亚纳地图的基础动力学有奇点（不连续性或临界点），并显示存在一个唯一的绝对连续不变的概率测度和相关的遍历属性，如拉伸指数衰减的相关性和拉伸指数大偏差。

Gibbs-Markov-Young structures with (stretched) exponential tail for partially hyperbolic attractors

We study partially hyperbolic sets $K$ on a Riemannian manifold $M$ whose tangent space splits as $T_K M=E^{cu}\oplus E^{s}$, for which the center-unstable direction $E^{cu}$ is non-uniformly expanding on some local unstable disk. We prove that the (stretched) exponential decay of recurrence times for an induced scheme can be deduced under the assumption of (stretched) exponential decay of the time that typical points need to achieve some uniform expanding in the center-unstable direction. This extends a result by Alves and Pinheiro to the (stretched) exponential case. As an application of our…

非均匀膨胀系统关联的衰减

Decay of correlations for nonuniformly expanding systems

我们估计一般非均匀膨胀动力系统的相关性衰减的速度，使用的时间估计系统需要真正扩大。我们的方法可以处理快速衰减，如指数或拉伸指数。特别证明了Alves-Viana映射的相关性在$O(e^{-c \sqrt{n}})$中衰减。

Large deviations for dynamical systems with stretched exponential decay of correlations

We obtain large deviations estimates for systems with stretched exponential decay of correlations, which improve the ones obtained in \cite{AFLV11}. As a consequence we obtain better large deviations estimates for Viana maps and get large deviations estimates for a class of intermittent maps with stretched exponential loss of memory.

Almost sure mixing rates for non-uniformly expanding maps

We consider random perturbations of non-uniformly expanding maps, possibly having a non-degenerate critical set. We prove that, if the Lebesgue measure of the set of points failing the non-uniform expansion or the slow recurrence to the critical set at a certain time, for almost all random orbits, decays in a (stretched) exponential fashion, then the decay of correlations along random orbits is stretched exponential, up to some waiting time. As applications, we obtain almost sure stretched exponential decay of random correlations for Viana maps, as for a class of non-uniformly expanding local …