Kolmogorov's Theorem for Low-Dimensional Invariant Tori of Hamiltonian\n Systems

2015/06/01 by П. И. Плотников, Plotnikov, Pavel, Ivan A. Kuznetsov +1
Mathematics · Physics and Astronomy · #37J40 #70H08 #70H15 #70H30 #70K43 #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1506.00383

openalex publication_date 2015/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper the problem of persistence of invariant tori under small\nperturbations of integrable Hamiltonian systems is considered. The existence of\none-to-one correspondence between hyperbolic invariant tori and critical points\nof the function \Ψ of two variables defined on semi-cylinder is\nestablished. It is proved that if unperturbed Hamiltonian has a saddle point,\nthen under arbitrary perturbations there persists at least one hyperbolic\ntorus.\n

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