Oscillatory Integrals and Phenomena Beyond all Algebraic Orders with Applications to Homoclinic Orbits in Reversible Systems /

• Main Author: Lombardi, Eric (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000.
• Edition: 1st ed. 2000.
• Series: Lecture Notes in Mathematics, 1741
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Statistical physics.; Dynamical systems.; Analysis.; Complex Systems.; Statistical Physics and Dynamical Systems.

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 giv...

Table of Contents:

• "Exponential tools" for evaluating oscillatory integrals
• Resonances of reversible vector fields
• Analytic description of periodic orbits bifurcating from a pair of simple purely imaginary eigenvalues
• Constructive floquet theory for periodic matrices near a constant one
• Inversion of affine equations around reversible homoclinic connections
• The 02+i? resonance
• The 02+i? resonance in infinite dimensions. Application to water waves
• The (i?0)2i?1 resonance.