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Communications in Mathematical Physics

, Volume 209, Issue 2, pp 353–392 | Cite as

A Geometric Approach to the Existence of Orbits with Unbounded Energy in Generic Periodic Perturbations by a Potential of Generic Geodesic Flows of ?2}

  • Amadeu Delshams
  • Rafael de la Llave
  • Tere M. Seara

Abstract:

We give a proof based in geometric perturbation theory of a result proved by J. N. Mather using variational methods. Namely, the existence of orbits with unbounded energy in perturbations of a generic geodesic flow in ?2 by a generic periodic potential.

Keywords

Perturbation Theory Variational Method Geometric Approach Periodic Potential Periodic Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Amadeu Delshams
    • 1
  • Rafael de la Llave
    • 2
  • Tere M. Seara
    • 1
  1. 1.Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647,¶08028 Barcelona, Spain. E-mail: amadeu@ma1.upc.es; tere@ma1.upc.esES
  2. 2.Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA.¶E-mail: llave@math.utexas.eduUS

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