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On the Absence of Anosov Factors for DA Local Diffeomorphisms
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 C1-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.
Related
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BibTeX
@misc{gu2026absence,
title = {{On the Absence of Anosov Factors for DA Local Diffeomorphisms}},
author = {Ruihao Gu and Mingyang Xia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10206},
eprint = {2609.10206},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10206},
}
RIS
TY - UNPB
TI - On the Absence of Anosov Factors for DA Local Diffeomorphisms
AU - Ruihao Gu
AU - Mingyang Xia
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10206
UR - https://arxiv.org/abs/2609.10206
AB - 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.
ER -