Bryuno Function and the Standard Map
Copyright policy )Bryuno Function and the Standard Map
For the standard map the homotopically non-trivial invariant curves of rotation number satisfying the Bryuno condition are shown to be analytic in the perturbative parameter, provided the latter is small enough. The radius of convergence of the Lindstedt series -- sometimes called critical function of the standard map -- is studied and the relation with the Bryuno function is derived: the logarithm of the radius of convergence plus twice the Bryuno function is proved to be bounded (from below and from above) uniformily in the rotation number.
120 K, Latex, 33 pages
real rotation numbers, Bryuno condition, FOS: Physical sciences, standard map, Nonlinear Sciences - Chaotic Dynamics, Lindstedt series, Dynamical aspects of twist maps, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Symplectic mappings, fixed points (dynamical systems), radius of convergence, Chaotic Dynamics (nlin.CD)
real rotation numbers, Bryuno condition, FOS: Physical sciences, standard map, Nonlinear Sciences - Chaotic Dynamics, Lindstedt series, Dynamical aspects of twist maps, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Symplectic mappings, fixed points (dynamical systems), radius of convergence, Chaotic Dynamics (nlin.CD)
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