Memoirs of the American Mathematical Society 1994; 191 pp; softcover Volume: 107 ISBN10: 082182581X ISBN13: 9780821825815 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/107/513
 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 ejectioncollision orbits of the perturbed system. Finally, they consider a class of nonHamiltonian 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
