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Construction of analytic KAM-surfaces and effective stability bounds. (English) Zbl 0657.58032
An effective method for finding of KAM-tori of Hamiltonian systems and canonical mappings closed to integrable ones is suggested. The method yields lower estimations for the break-down threshold of the tori under increasing of perturbative parameter. Computer-assisted applications to Chirikov-Green standard map \((x,y)\mapsto (x+y+\epsilon \sin x,\quad y+\epsilon \sin x)\) are given and the existence of “gold-mean” KAM- circles for complex values of \(\epsilon\) with \(| \epsilon | \leq 0.65\) is stated.
Reviewer: A.Givental’

MSC:
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
37C55 Periodic and quasi-periodic flows and diffeomorphisms
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
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