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

C. Chandré | Zendy

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

Author(s) -

C. Chandré

Publication year - 2002

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2002.2.457

Subject(s) - torus , renormalization group , mathematics , renormalization , invariant (physics) , mathematical physics , hamiltonian (control theory) , hamiltonian system , phase space , vector field , physics , mathematical analysis , quantum mechanics , geometry , mathematical optimization

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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