Oscillatory Integrals and Phenomena Beyond all Algebriac Orders With
During the last two decades, in several branches of science (water waves, crystal growth, travelling waves in one dimensional lattices, splitting of separatrices,...) different problems appeared in which the key point is the computation of exponentially s
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Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Eric Lombardi
Oscillatory Integrals and Phenomena Beyond all Algebraic Orders with Applications to Homoclinic Orbits in Reversible Systems
Springer
Author Eric Lombardi Institut Non Lineaire de Nice 1361 route des Lucioles Sophia Antipolis F-06560 Valbonne France E-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Lombarcli,Eric: Oscillatory integrals and phenomena beyond all algebraic orders: with applications to homoclinic orbits in reversible systems I Eric Lombarcli. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 2000 (Lecture notes in mathematics; 1741) ISBN 3-540-67785-2
Mathematics Subject Classification (2000): 34C23, 34C37, 37G25, 37G40, 76B25 ISSN 0075-8434 ISBN 3-540-67785-2 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag is a company in the BertelsmannSpringer publishing group. © Springer-Verlag Berlin Heidelberg 2000 Printed in Germany The use of general descriptive names, registered names, trademarks, 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. Typesetting: Camera-ready TEX output by the author Printed on acid-free paper SPIN: 10724282 41/3142/du
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List of Figures
1.1 Phase portrait for p = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Stable manifold of the periodic solution of the truncated system 4 1.3 02iw reversible resonance and (iWO)2iwl reversible resonance. . . . .. 11 1.4 0 2 reversible resonance and (iw)2 reversible resonance. . . . . . . . . .. 12 1.5 02iwoiwl reversible resonance 13
pit
Path r 1 · Description of f E H:'} Path re,R. Description of f E a.o Path r7j,R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Path r7j,7j' ,R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Step 1 : continuation in domain Va,r,E: Step 2 : continuation in E8,r, Domains i5 a,r,E: and i\r, Step 3 : continuation in E8,r,E: Description of fEE"; r r 2.12 Domain tr; r.s : 7f - e e r ± i _ e ) ) 2' , 27f 2 2 2.13 Continuation to E 8, 1. , along horizontal lines . . . . . . . . . . . . . . . . . .. 2.14 Continuation along flOriz
