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

• Author(s): Jaume Llibre, Ana Nunes,
• Publisher: American Mathematical Soc.
• Pages: 191
• ISBN_10: 082182581X
  ISBN_13: 9780821825815
  
• Language: en
• Categories: Mathematics / General , Mathematics / Differential Equations / General , Mathematics / Geometry / General , Mathematics / Functional Analysis , Mathematics / Topology ,

Description:... 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 criticalleaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonain 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.