Cargando…
Central Configurations, Periodic Orbits, and Hamiltonian Systems
The notes of this book originate from three series of lectures given at the Centre de Recerca Matemàtica (CRM) in Barcelona. The first one is dedicated to the study of periodic solutions of autonomous differential systems in Rn via the Averaging Theory and was delivered by Jaume Llibre. The second...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Springer Basel : Imprint: Birkhäuser,
2015.
|
| Edición: | 1st ed. 2015. |
| Colección: | Advanced Courses in Mathematics - CRM Barcelona,
|
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- 1 The Averaging Theory for Computing Periodic Orbits
- Introduction: the classical theory
- Averaging theory for arbitrary order and dimension
- Three applications of Theorem
- 2 Lectures on Central Configurations
- The n-body problem
- Symmetries and integrals
- Central configurations and self-similar solutions
- Matrix equations of motion
- Homographic motions of central configurations in Rd
- Albouy-Chenciner reduction and relative equilibria in Rd
- Homographic motions in Rd
- Central configurations as critical points
- Collinear central configurations
- Morse indices of non-collinear central configurations
- Morse theory for CC's and SBC's
- Dziobek configurations
- Convex Dziobek central configurations
- Generic finiteness for Dziobek central configurations
- Some open problems
- 3 Dynamical Properties of Hamiltonian Systems
- Introduction
- Low dimension
- Some theoretical results, their implementation and practical tools
- Applications to Celestial Mechanics.