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.

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Bibliographic Information

Book Title: Oscillatory Integrals and Phenomena Beyond all Algebraic Orders
Book Subtitle: with Applications to Homoclinic Orbits in Reversible Systems
Authors: Eric Lombardi
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0104102
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2000
Softcover ISBN: 978-3-540-67785-7Published: 28 August 2000
eBook ISBN: 978-3-540-44971-3Published: 06 May 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVIII, 418
Topics: Analysis, Complex Systems, Statistical Physics and Dynamical Systems

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Table of contents (9 chapters)

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