Umfang:
Online-Ressource (VIII, 232 p. 40 illus., 5 illus. in color, online resource)
Ausgabe:
1st ed. 2015
ISBN:
9783034809337
Serie:
Advanced Courses in Mathematics - CRM Barcelona
Inhalt:
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
Inhalt:
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
Anmerkung:
1 The Averaging Theory for Computing Periodic OrbitsIntroduction: 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.
Weitere Ausg.:
ISBN 9783034809320
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Llibre, Jaume, 1952 - Central configurations, periodic orbits, and hamiltonian systems Basel : Birkhäuser, 2015 ISBN 9783034809320
Sprache:
Englisch
DOI:
10.1007/978-3-0348-0933-7
URL:
Volltext
(lizenzpflichtig)
Mehr zum Autor:
Llibre, Jaume 1952-
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