Central Configurations, Periodic Orbits, and Hamiltonian Systems
Published on 18. December 2015
VIII, 232 pages
978-3-0348-0933-7 (ISBN)
Description
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 R n via the Averaging Theory and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying Central Configurations. The last one, by Carles Simó, describes the main mechanisms leading to a fairly global description of the dynamics in conservative systems.
The book is directed towards graduate students and researchers interested in dynamical systems, in particular in the conservative case, and aims at facilitating the understanding of dynamics of specific models. The results presented and the tools introduced in this book include a large range of applications.More details
Series
Edition
1st ed. 2015
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Primary & secondary/elementary & high school
Illustrations
VIII, 232 p. 40 illus., 5 illus. in color.
ISBN-13
978-3-0348-0933-7 (9783034809337)
DOI
10.1007/978-3-0348-0933-7
Schweitzer Classification
Other editions
Additional editions
Jaume Llibre | Richard Moeckel | Carles Simó
Central Configurations, Periodic Orbits, and Hamiltonian Systems
Book
12/2015
Birkhäuser
€32.09
Shipment within 10-15 days
Content
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.
