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Separatrix surfaces and invariant manifolds of a class of integrable Hamiltonian systems and their perturbations /
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
1994.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 513. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""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 â??[sub(HC)]""; ""2.1. The set A""; ""2.2. The set B""; ""2.3. The set Ï?(HC)""; ""2.4. Simple bifurcations""; ""3. Classification of the simple bifurcations""; ""3.1. The bifurcations of â??'[sub(HC) â?© Ï?(H,C)""; ""3.2. The bifurcations of â??'[sub(HC) â?© 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 foliationsCHAPTER 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