Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations

Llibre, Jaume & Ana Nunes

ISBN 10: 082182581X / ISBN 13: 9780821825815

Published by Amer Mathematical Society, 1994

About this Item

Text clean and solid; Memoirs of the American Mathematical Society Number 513; 9.92 X 6.77 X 0.47 inches; 191 pages.

Seller Inventory # 208611

Bibliographic Details

• Title: Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations
• Publisher: Amer Mathematical Society
• Publication Date: 1994
• Language: English
• ISBN 10: 082182581X
• ISBN 13: 9780821825815
• Binding: Paperback
• Condition: Very Good

About this title

Synopsis

This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the critical leaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonian perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of 'almost all' the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.