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Catalogue Information
Field name	Details
Dewey Class	515.352
Title	Central Configurations, Periodic Orbits, and Hamiltonian Systems ([EBook]) / by Jaume Llibre, Richard Moeckel, Carles Simó.
Author	Llibre, Jaume
Added Personal Name	Moeckel, Richard author.
Added Personal Name	Simó, Carles author.
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2015.
Publication	Basel : : Springer Basel : : Imprint: Birkhäuser, , 2015.
Physical Details	VIII, 232 p. 40 illus., 5 illus. in color. : online resource.
Series	Advanced courses in mathematics, CRM Barcelona 2297-0304
ISBN	9783034809337
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-0348-0933-7
Links to Related Works	Subject References: Differential Equations . Dynamical systems and ergodic theory . Dynamics . Ergodic theory . Mathematical Applications in the Physical Sciences . Mathematical Methods in Physics . Mathematical Physics . Mathematics . Ordinary differential equations . Physics . Authors: Llibre, Jaume . Moeckel, Richard . Simó, Carles . Corporate Authors: SpringerLink (Online service) . Series: Advanced courses in mathematics, CRM Barcelona . Classification: 515.352 .

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Central Configurations, Periodic Orbits, and Hamiltonian Systems

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