5 papers
Global periodic-data rigidity for irreducible toral automorphisms
Zhenqi Jenny Wang
We prove a global \(C^{1+\text{Hölder}}\)-rigidity theorem for Anosov diffeomorphisms of tori with irreducible linearization. Let \(f:\mathbb T^N\to\mathbb T^N\) be a \(C^2\) Anos…
Multiple mixing and multiple fractional cohomological equation: semisimple setting
Zhenqi Jenny Wang
The purpose of this paper is to develop a new effective approach to higher-order mixing in the semisimple setting. We prove effective exponential mixing of all orders for partially…
Multiple Fractional Cohomological Equations and Quantitative Mixing on Nilmanifolds
Zhenqi Jenny Wang
We develop a new analytic method for quantitative mixing of automorphisms on nilmanifolds. The method is based on the introduction and solvability of \emph{multiple fractional coho…
Local rigidity of weak or no hyperbolicity algebraic actions
Zhenqi Jenny Wang
In this paper we study rigidity properties of abelian \hyphenation{break-able}actions with weak or no hyperbolicty. We introduce a general strategy for proving local rig…
Local rigidity of higher rank partially hyperbolic algebraic actions
Zhenqi Jenny Wang
We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show local rigidity of abelian ergodic algebrai…