Parabolic dynamics and Anisotropic Banach spaces
speaker: Paolo Giulietti (Dipartimento di Matematica, Università di Pisa)abstract: We present recent results, joint work with C. Liverani. We investigate the relation between the distributions appearing in the study of ergodic averages of parabolic flows (e.g. in the work of Flaminio-Forni) and the ones appearing in the study of the statistical properties of hyperbolic dynamical systems (i.e. the eigendistributions of the transfer operator acting on suitable anisotropic Banach spaces). To avoid, as much as possible, technical issues that would cloud the basic idea, we limit ourselves to a simple flow on the torus. Our main result is that, roughly, the growth of ergodic averages of a class of parabolic flows is controlled by the eigenvalues of a suitable transfer operator associated to the renormalizing dynamics. The connection that we illustrate is expected to hold in considerable generality (see http:/arxiv.org abs1412.7181).
timetable:
Thu 30 Jun, 11:30 - 12:15, Aula Dini
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