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Oscillatory Integrals and Phenomena Beyond all Algebriac Orders

With Applications to Homoclinic Orbits in Reversible Systems

  • Authors
  • Eric Lombardi

Part of the Lecture Notes in Mathematics book series (LNM, volume 1741)

Table of contents

About this book

Introduction

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 small terms. This self-contained monograph gives new and rigorous mathematical tools which enable a systematic study of such problems. Starting with elementary illuminating examples, the book contains (i) new asymptotical tools for obtaining exponentially small equivalents of oscillatory integrals involving solutions of nonlinear differential equations; (ii) implementation of these tools for solving old open problems of bifurcation theory such as existence of homoclinic connections near resonances in reversible systems.

Keywords

Eigenvalue Oscillatory integrals differential equation exponential equivalents homoclinic connections reversible systems

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0104102
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-67785-7
  • Online ISBN 978-3-540-44971-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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