Seminari del Dipartimento

Analisi

I'll discuss an abstract KAM result on the existence of invariant tori for possibly infinite dimensional dynamical systems.
Differently from the classical Moser's approach, I'll show that in principle there is no need to impose the second Mel'nikov conditions but only to invert (in some appropriate norm) the linearized operator in the normal directions: in particular this means that the serious technical difficulties in small divisors problems are those appearing in forced cases.The latter statement is commonly believed to be true: the main purpose is indeed to prove it under the weakest possible assumptions.
The result is obtained in collaboration with R. Feola and M. Procesi.

 
org: PROCESI Michela