A New Proof of the Existence of Embedded Surfaces with Anosov Geodesic Flow

Authors

Victor J. Donnay, Bryn Mawr CollegeFollow

Document Type

Article

Version

Author's Final Manuscript

Publication Title

Regular and Chaotic Dynamics

Volume

23

Publication Date

2018

Abstract

We give a new proof of the existence of compact surfaces embedded in ℝ³ with Anosov geodesic flows. This proof starts with a noncompact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone condition. Using a sequence of explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov.

Citation

Donnay, Victor J. 2018. "A New Proof of the Existence of Embedded Surfaces with Anosov Geodesic Flow." Regular and Chaotic Dynamics 23.6: 685-694.

DOI

http://doi.org/10.1134/S1560354718060047