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KAM Theory Near Multiplicity One Resonant Surfaces in Perturbations of A-Priori Stable Hamiltonian Systems

Rudnev, M. and Wiggins, S. (2000) KAM Theory Near Multiplicity One Resonant Surfaces in Perturbations of A-Priori Stable Hamiltonian Systems. In: Mechanics: From Theory to Computation - Essays in Honor of Juan-Carlos Simo. Springer New York , New York, NY, pp. 379-411. ISBN 978-1-4612-7059-1.

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We consider a near-integrable Hamiltonian system in the action-angle variables with analytic Hamiltonian. For a given resonant surface of multiplicity one we show that near a Cantor set of points on this surface, whose remaining frequencies enjoy the usual diophantine condition, the Hamiltonian may be written in a simple normal form which, under certain assumptions, may be related to the class which, following Chierchia and Gallavotti [1994], we call a-priori unstable. For the a-priori unstable Hamiltonian we prove a KAM-type result for the survival of whiskered tori under the perturbation as an infinitely differentiable family, in the sense of Whitney, which can then be applied to the above normal form in the neighborhood of the resonant surface.

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Additional Information:© 2000 Springer Science+Business Media New York. Communicated by Jerrold Marsden. This paper is dedicated to the memory of Juan-Carlos Simo. S. Wiggins would like to acknowledge research support by the National Science Foundation, DMS-9403691.
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Subject Keywords:KAM theory; multiplicity-one resonance surface; whiskered tori; normal form; integrability on Cantor sets
Classification Code:MSC numbers: 58F05, 58F07, 58F27, 58F30, 58F36, 70H05, 70K30
Record Number:CaltechAUTHORS:20191008-091854205
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99140
Deposited By: Tony Diaz
Deposited On:08 Oct 2019 18:08
Last Modified:16 Nov 2021 17:44

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