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Regular and Chaotic Dynamics

, Volume 23, Issue 6, pp 685–694 | Cite as

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

  • Victor Donnay
  • Daniel Visscher
Article

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.

Keywords

geodesic flow embedded surfaces Anosov flow cone fields 

MSC2010 numbers

37D20 37D40 53D25 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Bryn Mawr CollegeBryn MawrUSA
  2. 2.Ithaca CollegeIthacaUSA

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