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© 2000

Oscillatory Integrals and Phenomena Beyond all Algebriac Orders

With Applications to Homoclinic Orbits in Reversible Systems

  • Authors
Book

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

  • Book Title Oscillatory Integrals and Phenomena Beyond all Algebriac Orders
  • Book Subtitle With Applications to Homoclinic Orbits in Reversible Systems
  • Authors Eric Lombardi
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI https://doi.org/10.1007/BFb0104102
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-67785-7
  • eBook ISBN 978-3-540-44971-3
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XVIII, 418
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
    Complex Systems
    Statistical Physics and Dynamical Systems
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