On transversal Hölder regularity for flat Wieler solenoids

Pub Date : 2024-09-10 DOI:10.1017/etds.2024.41
RODRIGO TREVIÑO
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Abstract

This paper studies various aspects of inverse limits of locally expanding affine linear maps on flat branched manifolds, which I call flat Wieler solenoids. Among the aspects studied are different types of cohomologies, the rates of mixing given by the Ruelle spectrum of the hyperbolic map acting on this space, and solutions of the cohomological equation in primitive substitution subshifts for Hölder functions. The overarching theme is that considerations of $\alpha $ -Hölder regularity on Cantor sets go a long way.
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论平面维勒孤岛的横向赫尔德正则性
本文研究了平面分支流形(我称之为平面维勒孤岛)上局部膨胀仿射线性映射的逆极限的各个方面。研究的方面包括不同类型的同调、作用于该空间的双曲映射的鲁埃尔谱给出的混合率,以及霍尔德函数的原始置换子移动中的同调方程的解。总的主题是,在康托集上考虑$\alpha $ -霍尔德正则性有很长的路要走。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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