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Anosov Diffeomorphisms of Finite-Type Surfaces
Abstract
We prove that a complete surface of finite topological type satisfying Condition A is homeomorphic to the two-torus. More generally, we show that an isolated planar end of a complete open surface satisfying Condition A cannot be periodic under the induced action on the space of ends. Condition A includes dense periodic points, a uniformly hyperbolic splitting into one-dimensional subbundles for a complete metric, and invariant line fields that uniquely integrate to transverse stable and unstable foliations. These results give a partial answer to the question of whether a complete surface satisfying Condition A must be compact.
Related
- Codimension-one holomorphic Anosov diffeomorphisms
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- On the Absence of Anosov Factors for DA Local Diffeomorphisms
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BibTeX
@misc{ures2026anosov,
title = {{Anosov Diffeomorphisms of Finite-Type Surfaces}},
author = {Raúl Ures and Tongyao Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18253},
eprint = {2609.18253},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18253},
}
RIS
TY - UNPB
TI - Anosov Diffeomorphisms of Finite-Type Surfaces
AU - Raúl Ures
AU - Tongyao Yu
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18253
UR - https://arxiv.org/abs/2609.18253
AB - We prove that a complete surface of finite topological type satisfying Condition A is homeomorphic to the two-torus. More generally, we show that an isolated planar end of a complete open surface satisfying Condition A cannot be periodic under the induced action on the space of ends. Condition A includes dense periodic points, a uniformly hyperbolic splitting into one-dimensional subbundles for a complete metric, and invariant line fields that uniquely integrate to transverse stable and unstable foliations. These results give a partial answer to the question of whether a complete surface satisfying Condition A must be compact.
ER -