國立虎尾科技大學 |

Central configurations, periodic orbits, and Hamiltonian systems

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Central configurations, periodic orbits, and Hamiltonian systems/ by Jaume Llibre, Richard Moeckel, Carles Simo.
作者:	Llibre, Jaume.
其他作者:	Moeckel, Richard.
出版者:	Basel :Springer Basel : : 2015.,
面頁冊數:	viii, 232 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Differentiable dynamical systems. -
電子資源:	http://dx.doi.org/10.1007/978-3-0348-0933-7
ISBN:	9783034809337

Central configurations, periodic orbits, and Hamiltonian systems
Llibre, Jaume.

Central configurations, periodic orbits, and Hamiltonian systems[electronic resource] /by Jaume Llibre, Richard Moeckel, Carles Simo. - Basel :Springer Basel :2015. - viii, 232 p. :ill. (some col.), digital ;24 cm. - Advanced courses in mathematics - CRM Barcelona,2297-0304. - Advanced courses in mathematics, CRM Barcelona..

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.

The notes of this book originate from three series of lectures given at the Centre de Recerca Matematica (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 Simo, 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.

ISBN: 9783034809337

Standard No.: 10.1007/978-3-0348-0933-7doiSubjects--Topical Terms:

528273
Differentiable dynamical systems.

LC Class. No.: QA614.8

Dewey Class. No.: 515.39

Central configurations, periodic orbits, and Hamiltonian systems
LDR:02905nam a2200325 a 4500 001 838990
003 DE-He213
005 20160512130958.0
006 m d
007 cr nn 008maaau
008 160616s2015 sz s 0 eng d
020 $a 9783034809337 $q (electronic bk.)
020 $a 9783034809320 $q (paper)
024 7 $a 10.1007/978-3-0348-0933-7 $2 doi
035 $a 978-3-0348-0933-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA614.8
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.39 $2 23
090 $a QA614.8 $b .L791 2015
100 1 $a Llibre, Jaume. $3 1021384
245 1 0 $a Central configurations, periodic orbits, and Hamiltonian systems $h [electronic resource] / $c by Jaume Llibre, Richard Moeckel, Carles Simo.
260 $a Basel : $b Springer Basel : $b Imprint: Birkhauser, $c 2015.
300 $a viii, 232 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Advanced courses in mathematics - CRM Barcelona, $x 2297-0304
505 0 $a 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.
520 $a The notes of this book originate from three series of lectures given at the Centre de Recerca Matematica (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 Simo, 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.
650 0 $a Differentiable dynamical systems. $3 528273
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
650 2 4 $a Mathematical Methods in Physics. $3 670749
700 1 $a Moeckel, Richard. $3 1070462
700 1 $a Simo, Carles. $3 1070463
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Advanced courses in mathematics, CRM Barcelona. $3 1065979
856 4 0 $u http://dx.doi.org/10.1007/978-3-0348-0933-7
950 $a Mathematics and Statistics (Springer-11649)