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Renormalization and Periodic Orbits¶for Hamiltonian Flows

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Abstract:

We consider a renormalization group transformation for analytic Hamiltonians in two or more dimensions, and use this transformation to construct invariant tori, as well as sequences of periodic orbits with rotation vectors approaching that of the invariant torus. The construction of periodic and quasiperiodic orbits is limited to near-integrable Hamiltonians. But as a first step toward a non-perturbative analysis, we extend the domain of to include any Hamiltonian for which a certain non-resonance condition holds.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA, , , , , , US

    Juan J. Abad & Hans Koch

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  1. Juan J. Abad
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  2. Hans Koch
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Received: 5 October 1999 / Accepted: 2 February 2000

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Abad, J., Koch, H. Renormalization and Periodic Orbits¶for Hamiltonian Flows. Comm Math Phys 212, 371–394 (2000). https://doi.org/10.1007/s002200000218

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  • DOI: https://doi.org/10.1007/s002200000218

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