论文标题
分段的平衡状态的定量统计稳定性部分双曲图
Quantitative statistical stability for the equilibrium states of piecewise partially hyperbolic maps
论文作者
论文摘要
我们考虑一类包含一组分段的内态性，部分双曲动力学半偶联到非均匀扩展的地图。我们的目标是研究一类内态性，这些内态保留几乎均匀签约的叶面，可能的不连续性与收缩方向平行。我们应用光谱间隙属性和$ζ$-Hölder的规律性，其均衡状态的分解属性证明了定量统计稳定性声明。更确切地说，在尺寸$δ$系统的确定性扰动下，我们表明$ f $ invariant度量因合适的各向异性规范而不断变化。此外，我们证明，对于某些有趣的类扰动，其连续性模量为$ O（δ^ζ\logδ）$。本文已被接受在离散和连续的动态系统杂志上发表。
We consider a class of endomorphisms that contains a set of piecewise partially hyperbolic dynamics semi-conjugated to non-uniformly expanding maps. Our goal is to study a class of endomorphisms that preserve a foliation that is almost everywhere uniformly contracted, with possible discontinuity sets parallel to the contracting direction. We apply the spectral gap property and the $ζ$-Hölder regularity of the disintegration of its equilibrium states to prove a quantitative statistical stability statement. More precisely, under deterministic perturbations of the system of size $δ$, we show that the $F$-invariant measure varies continuously with respect to a suitable anisotropic norm. Moreover, we prove that for certain interesting classes of perturbations, its modulus of continuity is $O(δ^ζ\log δ)$. This article has been accepted for publication in the Discrete and Continuous Dynamical Systems journal.
