Rigidity for Some Cases of Anosov Endomorphisms of Torus

Autor:	Micena, Fernando
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	We obtain smooth conjugacy between non-necessarily special Anosov endomorphisms in the conservative case. Among other results, we prove that a strongly special $C^{\infty}-$Anosov endomorphism of $\mathbb{T}^2$ and its linearization are smoothly conjugated since they have the same periodic data. Assuming that for a strongly special $C^{\infty}-$Anosov endomorphism of $\mathbb{T}^2$ every point is regular (in Oseledec's Theorem sense), then we obtain again smooth conjugacy with its linearization. We also obtain some results on local rigidity of linear Anosov endomorphisms of $d-$torus, where $d \geq 3,$ under periodic data assumption. The study of differential equations defined on invariant leaves plays an important role in rigidity problems such as those treated here. Comment: We state Theorem A in a more broad context using the same previous proof. We put a little more detail in the construction to prove Theorem B
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.00407 Zobrazit plný text záznamu View this record from Arxiv