## Abstract

A new method is developed for characterizing the evolution of invariant tori of slowly varying perturbations of completely integrable (in the sense of Liouville-Arnold [1-3]) Hamiltonian systems on cotangent phase spaces. The method is based on Cartan's theory of integral submanifolds, and it provides an algebro-analytic approach to the investigation of the embedding [4-10] of the invariant tori in phase space that can be used to describe the structure of quasi-periodic solutions on the tori. In addition, it leads to an adiabatic perturbation theory [3,12,13] of the corresponding Lagrangian asymptotic submanifolds via the Poincaré-Cartan approach [4], a new Poincaré-Melnikov type [5,11,14] procedure for determining stability, and fresh insights into the existence problem for adiabatic invariants [2,3] of the Hamiltonian systems under consideration.

Original language | English (US) |
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Pages (from-to) | 171-182 |

Number of pages | 12 |

Journal | Reports on Mathematical Physics |

Volume | 44 |

Issue number | 1-2 |

State | Published - Jan 1 1999 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics