Oscillatory integrals and phenomena beyond all algebraic orders : with applications to homoclinic orbits in reversible systems / Eric Lombardi.

Format:

Book

Author/Creator:

Lombardi, Eric, 1968-

Contributor:

George R. Fink Memorial Fund.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1741.

Lecture notes in mathematics, 0075-8434 ; 1741

Language:

English

Subjects (All):

Bifurcation theory.

Differential equations, Nonlinear--Numerical solutions.

Differential equations, Nonlinear.

Differentiable dynamical systems.

Physical Description:

xv, 412 pages : illustrations ; 24 cm.

Place of Publication:

Berlin ; New York : Springer, [2000]

Summary:

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

Notes:

Includes bibliographical references (pages [405]-410) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the George R. Fink Memorial Fund.

ISBN:

3540677852

OCLC:

44550604