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

Intro -- TABLE OF CONTENTS -- CHAPTER I: INTRODUCTION AND STATEMENT OF THE RESULTS -- CHAPTER II: BIFURCATIONS -- 1. Hamiltonian systems with two degrees of freedom associated to central potentials -- 1.1. Preliminary results on Hamiltonian systems -- 1.2. Definitions and basic properties -- 2. Study of the bifurcation set ∑[sub(HC)] -- 2.1. The set A -- 2.2. The set B -- 2.3. The set σ(HC) -- 2.4. Simple bifurcations -- 3. Classification of the simple bifurcations -- 3.1. The bifurcations of ∑'[sub(HC) ∩ σ(H,C) -- 3.2. The bifurcations of ∑'[sub(HC) ∩ B -- 3.3. Stability of the simple bifurcations -- CHAPTER III: SEPARATRIX SURFACES AND FOLIATIONS OF THE ENERGY LEVELS -- 1. Regularization of the singularities -- 1.1. Introduction of McGehee's coordinates -- 1.2. Regularization of collision -- 1.3. Regularization of infinity -- 1.4. The manifolds W[sup(u,s)](S‌[sup(+,…)]) -- 2. Separatrix surfaces -- 2.1. Simple separatrix surfaces -- 2.2. Characterization of the separatrix surfaces -- 3. Simple foliations -- 3.1. Simple energy values -- 3.2. Classification of the simple foliations -- 3.3. Stability of the simple foliations -- CHAPTER IV: THE PERTURBEB HAMILTONIAN -- 1. Persistence of the separatrix structures -- 1.1. Persistence of the circular orbits -- 1.2. Persistence of the singularity manifolds -- 1.3. Persistence of the invariant manifolds associated to invariant circles -- 2. Transversal ejection - collision orbits -- 3. Persistence of invariant tori and cylinders -- REFERENCES.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.