Oscillatory Integrals and Phenomena Beyond all Algebraic Orders
Edition: 1 edition
Publisher: Springer
Published: October 2, 2000
Language: eng
Format: Paperback
Number of pages: 412
ISBN-13: 9783540677857
Subjects: Differential Equations; Stochastics; Science/Mathematics; Differential equations, Nonlinear; Mathematics; Physics; Numerical solutions; General; Mathematics / Differential Equations; Mathematics / Mathematical Analysis; Oscillatory integrals; exponential equivalents; homoclinic connections; reversible systems; Differentiable dynamical syste; Bifurcation theory; Differentiable dynamical systems; Differential equations, Nonlin
First sentence: This work is devoted to "phenomena beyond any algebraic order" in dynamical systems.
Description: 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.