Multiscale time averaging, Reloaded

2012/07/04 by Shmuel Fishman, Avy Soffer, Fishman, Shmuel +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #math-ph #math.DS #math.MP

paper · pdf · doi:10.48550/arxiv.1207.1125

revised version, to appear in SIAM J. of Math Analysis. Corrected problem with bibliography

arxiv created 2013/08/15 · arxiv updated 2013/08/16

Abstract

We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary order. Here, we consider as an example the problem of finite dimensional conservative dynamical system, which is quasiperiodic and dominated by slow frequencies, leading to small divisor problems in perturbative schemes.

Citations

• Resonances, radiation damping and instabilitym in Hamiltonian nonlinear wave equations
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

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