Mathematical Sciences: Dynamical Systems with Infinitely Many Degrees of Freedom in Mathematical Physics

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This proposal is concerned with the dynamics of some partial differential equations that arise in mathematical physics. Problems concerning the method of accelerated convergence, KAM theory, center manifolds, and normal forms are complicated in the finite dimensional case. In infinite dimensions there are additional complications such as the appearance of zero divisors rather that just small divisors. Dynamical systems is a geometric rigorous way of describing the behavior of solutions of systems of ordinary or partial differential equations which can not be solved explicitly. The ability to accurately describe the behavior of such solutions has important ramifications in understanding the world around us.