Smooth rigidity for 3-dimensional volume preserving Anosov flows and weighted marked length spectrum rigidity

Autor:	Gogolev, Andrey, Hertz, Federico Rodriguez
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	Let $X_1^t$ and $X_2^t$ be volume preserving Anosov flows on a 3-dimensional manifold $M$. We prove that if $X_1^t$ and $X_2^t$ are $C^0$ conjugate then the conjugacy is, in fact, smooth, unless $M$ is a mapping torus of an Anosov automorphism of $\mathbb T^2$ and both flows are constant roof suspension flows. We deduce several applications. Among them is a new result on rigidity of Anosov diffeorphisms on $\mathbb T^2$ and a new "weighted" marked length spectrum rigidity result for surfaces of negative curvature. Comment: V2: 27 pages, one figure. The weighted marked length spectrum rigidity is improved to allow weights which are not necessarily positive. We now have an optimal version of this result
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.02295 Zobrazit plný text záznamu View this record from Arxiv