Renormalization of quasiperiodic dynamics
2009-02-20 14:00 2009-02-20 15:00 2009-02-20 14:00 .. 15:00
by João Lopes-Dias (Departamento de Matemática, ISEG, Portugal)
We will discuss the construction of renormalization operators acting on vector fields and their application to dynamical systems problems. We will be mainly interested on the stability of diophantine invariant tori in Hamiltonian flows close to integrable and related systems. The renormalization relies fundamentally on a strongly convergent multidimensional continued fraction expansion based in the geodesic flow of the homogeneous space of unimodular lattices, which we will discuss.