Work

On the Absence of Anosov Factors for DA Local Diffeomorphisms

Year: 2026

Type: preprint

Abstract: We give a class of local diffeomorphisms which are homotopic to toral hyperbolic endomorphisms, but which are not topologically semi-conjugate, within the homotopic class of the identity, to any Anosov local diffeomorphism. In particular, we show that for a non-invertible partially hyperbolic $C^1$-smooth local diffeomorphism with expanding directions on the $2$-torus, if it is semi-conjugate to an Anosov local diffeomorphism, then it is also an Anosov local diffeomorphism.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.10206

Authors: Gu, Ruihao, Xia, Mingyang

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Award: G8998874865

OpenAlex ID: W7212118635

Cites: 2

Cited by:

Related to: 10