Invariant tori for two-dimensional non-integrable Hamiltonians
type: Item
instance of: scholarly article
title: Invariant tori for two-dimensional non-integrable Hamiltonians
zbMATH Open document ID: 0647.58021
DOI: 10.1016/0003-4916(88)90005-X
published in: Annals of Physics
publication date: 1988-01-01T00:00:00Z
review text: The invariant tori of a two-dimensional non-integrable Hamiltonian form families which can be parametrized by the energy and the rotation number. Within each family, the variation with energy is continuous, the variation with rotation number is governed by the KAM theorem and everywhere discontinuous. In order to calculate the tori numerically, we approximate them by highly winding periodic orbits, and we give a criterion for the validity of this approximation. For one particular Hamiltonian, we study the family of tori which connects two distinct families of periodic trajectories. As a by-product of this calculation, we draw the curve bounding the ``mostly regular'' region, on a plot whose coordinates are the two partial periods of the tori.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 4056622
zbMATH Keywords: non-integrable Hamiltonian form
zbMATH Keywords: energy
zbMATH Keywords: rotation number
zbMATH Keywords: highly winding periodic orbits
author: M. A. M. de Aguiar
author: M. Baranger
MaRDI profile type: Publication
cites work: Q4065809
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full work available at URL: 0003-4916(88)90005-x
OpenAlex ID: W2085471496
description: scientific article; zbMATH DE number 4056622