Exponential asymptotics of oscillatory integrals. Application to the problem of persistence of homoclinic connections for the 02iω resonance

Exponential asymptotics of bi-oscillator

Exponential asymptotics of bi-oscillatory integrals. Application to the problem of persistence of homoclinic connections for the (iω0)2iω1 resonance

✍ Eric Lombardi 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 479 KB

We explain in this Note how to obtain an exponentially small equivalent of a bioscillatory integral when it involves solutions of a nonlinear differential equation. The method proposed in this Note enables us to study the problem of existence of homoclinic connections for vector fields admitting a (