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

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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.

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Authors and Affiliations

  1. Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647,¶08028 Barcelona, Spain. E-mail: amadeu@ma1.upc.es; tere@ma1.upc.es, , , , , , ES

    Amadeu Delshams & Tere M. Seara

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA.¶E-mail: llave@math.utexas.edu, , , , , , US

    Rafael de la Llave

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  1. Amadeu Delshams
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  2. Rafael de la Llave
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  3. Tere M. Seara
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Received: 22 September 1998 / Accepted: 2 August 1999

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Delshams, A., de la Llave, R. & Seara, T. A Geometric Approach to the Existence of Orbits with Unbounded Energy in Generic Periodic Perturbations by a Potential of Generic Geodesic Flows of ?2} . Comm Math Phys 209, 353–392 (2000). https://doi.org/10.1007/PL00020961

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  • DOI: https://doi.org/10.1007/PL00020961

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