Oscillatory Integrals and Phenomena Beyond all Algebriac Orders
Lombardi, Eric.
Oscillatory Integrals and Phenomena Beyond all Algebriac Orders With Applications to Homoclinic Orbits in Reversible Systems / [electronic resource] : by Eric Lombardi. - XVIII, 418 p. online resource. - Lecture Notes in Mathematics, 1741 0075-8434 ; . - Lecture Notes in Mathematics, 1741 .
"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.
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.
9783540449713
10.1007/BFb0104102 doi
Global analysis (Mathematics).
Statistical physics.
Analysis.
Complex Systems.
Statistical Physics and Dynamical Systems.
QA299.6-433
515
Oscillatory Integrals and Phenomena Beyond all Algebriac Orders With Applications to Homoclinic Orbits in Reversible Systems / [electronic resource] : by Eric Lombardi. - XVIII, 418 p. online resource. - Lecture Notes in Mathematics, 1741 0075-8434 ; . - Lecture Notes in Mathematics, 1741 .
"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.
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.
9783540449713
10.1007/BFb0104102 doi
Global analysis (Mathematics).
Statistical physics.
Analysis.
Complex Systems.
Statistical Physics and Dynamical Systems.
QA299.6-433
515