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

C. Chandre

doi:10.3934/dcdsb.2002.2.457

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2002, Volume 2, Issue 3: 457-465. Doi: 10.3934/dcdsb.2002.2.457

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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

Received: May 31, 2001

Revised: November 30, 2001

Published: July 2002

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Abstract

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.

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Mathematics Subject Classification: 37E20.

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