Magistrelli, Elisa (2011) KAM Theory for PDEs. [Tesi di dottorato] (Unpublished)
Download (2MB) | Preview
|Item Type:||Tesi di dottorato|
|Uncontrolled Keywords:||KAM, PDE, resonant, degenerate|
|Date Deposited:||07 Dec 2011 14:25|
|Last Modified:||30 Apr 2014 19:49|
This thesis is concerned with KAM theory for Hamiltonian partial differential equations. This theory answers to the following matter: since the solutions of a linear equation are periodic, quasi periodic or almost periodic (for they are superpositions of periodic motions), the problem is to investigate what happens when we add a (sufficiently) small nonlinearity. This thesis contains two new results: an abstract KAM theorem for degenerate infinite--dimensional systems, with an application to the nonlinear wave equation, and a KAM theorem for a completely resonant nonlinear Schr\"odinger equation.
Actions (login required)