Oscillatory Integrals and Phenomena Beyond all Algebraic Orders: with Applications to Homoclinic Orbits in Reversible 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 gives new and rigorous mathematical tools which enable a systematic study of such problems.