Abstract:
The celebrated Arnold-Liouville theorem provides a beautiful description of integrable Hamilton-
ian systems stating that the dynamics on compact invariant sets is conjugated to a linear flow on the
torus Tn := Rn/Zn. It is then clear that in trying to generalize this statement to Hamiltonian sys-
tems with infinitely many degrees of freedom, one has first to face with the issue of understanding
linear flows on the infinite torus. In this talk we discuss the simple characterization occurring in finite
dimension and why it fails to apply in an infinite-dimensional setting. Then, we use Pontryagin’s
theory of locally compact abelian groups in order to understand the dynamics and we also discuss an
analogy with the finite dimensional case, namely unique ergodicity in the absence of resonances.
Il seminario è organizzato dai dottorandi di Matematica e si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, via della Vasca Navale 84, aula C.
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