By Eric Lombardi
Over the past twenty years, in numerous branches of technological know-how (water waves, crystal progress, vacationing waves in a single dimensional lattices, splitting of separatrices,...) diversified difficulties seemed within which the major aspect is the computation of exponentially small phrases. This self-contained monograph supplies new and rigorous mathematical instruments which allow a scientific learn of such difficulties. beginning with uncomplicated illuminating examples, the ebook comprises (i) new asymptotical instruments for acquiring exponentially small equivalents of oscillatory integrals regarding suggestions of nonlinear differential equations; (ii) implementation of those instruments for fixing outdated open difficulties of bifurcation idea corresponding to lifestyles of homoclinic connections close to resonances in reversible structures.
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