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Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations
Jaume Llibre and Ana Nunes
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Memoirs of the American Mathematical Society
1994; 191 pp; softcover
Volume: 107
ISBN-10: 0-8218-2581-X
ISBN-13: 978-0-8218-2581-5
List Price: US$42
Individual Members: US$25.20
Institutional Members: US$33.60
Order Code: MEMO/107/513
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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.

Readership

Graduate students and researchers with an interest in dynamical systems and mathematical physics.

Table of Contents

  • Introduction and statement of the results
  • Bifurcations
  • Separatrix surfaces and foliations of the energy levels
  • The perturbed Hamiltonian
  • References
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