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arXiv · 2609.10206

On the Absence of Anosov Factors for DA Local Diffeomorphisms

Ruihao Gu·Mingyang Xia
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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.

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Ruihao Gu, Mingyang Xia. 2026-09-09. On the Absence of Anosov Factors for DA Local Diffeomorphisms. https://arxiv.org/abs/2609.10206

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