Seminari del Dipartimento
Analisi An infinite dimensional KAM theorem with application to 2-d completely resonant beam equation Shidi Zhou 22-11-2017 - 16:00 Largo San Leonardo Murialdo,1 - Pal.C - AULA 311
In this talk we shall consider the 2-dimensional completely resonant beam equation with cubic nonlinearity on Tˆ2. We prove the existence of the quasi-periodic solutions, which lie in a special subspace of Lˆ2 (Tˆ2). We view the equation as an infinite dimensional Hamiltonian system, and write the Hamiltonian of the equation as an angle-dependent block-diagonal normal form plus a small perturbation with some regularity. By establishing an abstract KAM theorem, we prove the existence of a class of invariant tori of this system, which implies the existence of a class of small-amplitude quasi-periodic solutions of the equation. In the KAM iteration, the measure estimate is reached by making use of the regularity of the nonlinearity. |