Integration of Hamiltonian Systems
In this chapter, we illustrate the various ways to “integrate” a Hamiltonian system on two examples with two degrees of freedom: the cubic (HH3) and quartic (HH4) Hénon-Heiles Hamiltonians. These various ways to integrate are ∘ (Liouville integrability) t
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Robert Conte Micheline Musette
The Painlevé Handbook Second Edition
Mathematical Physics Studies Series Editors Giuseppe Dito, Dijon, France Edward Frenkel, Berkeley, CA, USA Sergei Gukov, Pasadena, CA, USA Yasuyuki Kawahigashi, Tokyo, Japan Maxim Kontsevich, Bures-sur-Yvette, France Nicolaas P. Landsman, Nijmegen, The Netherlands Bruno Nachtergaele, Davis, CA, USA
The series publishes original research monographs on contemporary mathematical physics. The focus is on important recent developments at the interface of Mathematics, and Mathematical and Theoretical Physics. These will include, but are not restricted to: application of algebraic geometry, D-modules and symplectic geometry, category theory, number theory, low-dimensional topology, mirror symmetry, string theory, quantum field theory, noncommutative geometry, operator algebras, functional analysis, spectral theory, and probability theory.
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Robert Conte • Micheline Musette
The Painlevé Handbook Second Edition
Robert Conte Centre Giovanni Borelli CNRS, ENS Paris-Saclay Université Paris-Saclay Cachan Cedex, France
Micheline Musette Dienst Theoretische Natuurkunde (TENA) Vrije Universiteit Brussel Brussels, Belgium
Department of Mathematics The University of Hong Kong Pokfulam, Hong Kong
ISSN 0921-3767 ISSN 2352-3905 (electronic) Mathematical Physics Studies ISBN 978-3-030-53339-7 ISBN 978-3-030-53340-3 (eBook) https://doi.org/10.1007/978-3-030-53340-3 1st edition: © Canopus Publishing Limited 2008 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Les cas où l’on peut intégrer une équation différentielle sont ext
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