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August  2002, 2(3): 457-465. doi: 10.3934/dcdsb.2002.2.457

Renormalization for cubic frequency invariant tori in Hamiltonian systems with two degrees of freedom

C. Chandre 1,

1. 

Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, United States

Received  June 2001 Revised  December 2001 Published  May 2002

We consider the break-up of invariant tori in Hamiltonian systems with two degrees of freedom with a frequency which belongs to a cubic field. We define and construct renormalization-group transformations in order to determine the threshold of the break-up of these tori. A first transformation is defined from the continued fraction expansion of the frequency, and a second one is defined with a fixed frequency vector in a space of Hamiltonians with three degrees of freedom.
Keywords: Hamiltonian systems., invariant tori, Renormalization.
Mathematics Subject Classification: 37E2.
Citation: C. Chandre. Renormalization for cubic frequency invariant tori in Hamiltonian systems with two degrees of freedom. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 457-465. doi: 10.3934/dcdsb.2002.2.457
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