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On the width of the instability zone near the separatrices of a standard mapping. (English. Russian original) Zbl 0733.58038
Sov. Math., Dokl. 42, No. 1, 5-9 (1991); translation from Dokl. Akad. Nauk SSSR 313, No. 2, 268-272 (1990).
The instability zone for a system with two degrees of freedom is characterized by the author as a narrow neighbourhood of the separatrices which are squeezed between tori invariant under small perturbations. All the chaotic phenomena occur in this zone.
The upper and lower bounds for the width of such zones are obtained explicitly in this paper.
Reviewer: J.Andres (Olomouc)

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion