Elementary Symplectic Topology and Mechanics
This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and ot
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Franco Cardin
Elementary Symplectic Topology and Mechanics
Lecture Notes of the Unione Matematica Italiana
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Editorial Board
Ciro Ciliberto (Editor in Chief) Dipartimento di Matematica Universita’ di Roma Tor Vergata Via della Ricerca Scientifica 00133 Roma (Italia) e-mail: [email protected] Susanna Terracini (Co-editor in Chief) Università degli Studi di Torino Dipartimento di Matematica “Giuseppe Peano” Via Carlo Alberto 10 10123 Torino, Italy e-mail: [email protected] Adolfo Ballester-Bollinches Department d’Àlgebra Facultat de Matemàtiques Universitat de València Dr. Moliner, 50 46100 Burjassot (València) Spain e-mail: [email protected] Annalisa Buffa IMATI – C.N.R. Pavia Via Ferrata 1 27100 Pavia, Italy e-mail: [email protected] Lucia Caporaso Dipartimento di Matematica Università Roma Tre Largo San Leonardo Murialdo I-00146 Roma, Italy e-mail: [email protected] Fabrizio Catanese Mathematisches Institut Universitätstraße 30 95447 Bayreuth, Germany e-mail: [email protected] Corrado De Concini Dipartimento di Matematica Università di Roma “La Sapienza” Piazzale Aldo Moro 5 00185 Roma, Italy e-mail: [email protected] Camillo De Lellis Institut fuer Mathematik Universitaet Zuerich Winterthurerstrasse 190 The Editorial Policy can be found at the back of the volume.
CH-8057 Zuerich, Switzerland e-mail: [email protected] Franco Flandoli Dipartimento di Matematica Applicata Università di Pisa Via Buonarroti 1c 56127 Pisa, Italy e-mail: [email protected] Angus Mcintyre Queen Mary University of London School of Mathematical Sciences Mile End Road London E1 4NS United Kingdom e-mail: [email protected] Giuseppe Mingione Dipartimento di Matematica e Informatica Università degli Studi di Parma Parco Area delle Scienze, 53/a (Campus) 43124 Parma, Italy e-mail: [email protected] Mario Pulvirenti Dipartimento di Matematica, Università di Roma “La Sapienza” P.le A. Moro 2 00185 Roma, Italy e-mail: [email protected] Fulvio Ricci Scuola Normale Superiore di Pisa Piazza dei Cavalieri 7 56126 Pisa, Italy e-mail: [email protected] Valentino Tosatti Northwestern University Department of Mathematics 2033 Sheridan Road Evanston, IL 60208 USA e-mail: [email protected] Corinna Ulcigrai Forschungsinstitut für Mathematik HG G 44.1 Rämistrasse 101 8092 Zürich, Switzerland e-mail: [email protected]
Franco Cardin
Elementary Symplectic Topology and Mechanics
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Franco Cardin Dipartimento di Matematica Padova Italy
ISSN 1862-9113 ISBN 978-3-319-11025-7 ISBN 978-3-319-11026-4 (eBook) DOI 10.1007/978-3-319-11026-4 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014955673 Mathematics Subject Classification (2010): 53D05, 53D12, 37J05, 37J10, 35F21, 58E05, 53Z05 © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether
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