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Central Configurations, Periodic Orbits, and Hamiltonian Systems (Advanced Courses in Mathematics - CRM Barcelona)

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en Limba Engleză Carte Paperback – 29 Dec 2015
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 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.
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Specificații

ISBN-13: 9783034809320
ISBN-10: 3034809328
Pagini: 240
Ilustrații: Bibliographie
Dimensiuni: 168 x 240 x 13 mm
Greutate: 4.15 kg
Ediția: 1st ed. 2015
Editura: Springer
Colecția Birkhäuser
Seria Advanced Courses in Mathematics - CRM Barcelona

Locul publicării: Basel, Switzerland

Public țintă

Graduate

Cuprins

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.

Textul de pe ultima copertă

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 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.

Caracteristici

Provides applications to the study of periodic solutions for some well know differential equations and Hamiltonian systems
Includes new ideas and techniques for central configurations in spaces with dimension bigger than three
Presents invariant objects in dynamical systems in a unique combination of analytical and geometrical aspects