Dynamical Systems Seminar

For rapidly mixing nonuniformly hyperbolic dynamical systems, Hölder observables are known to satisfy the central limit theorem (convergence in distribution to a normal distribution). In addition, such observables converge in a strong sense to Brownian motion (Melbourne & Nicol, 2009).

For slowly mixing systems, such as Pomeau-Manneville intermittency maps, the central limit theorem is replaced by the appropriate stable law, and it is natural to expect convergence to the corresponding Lévy process. However, such convergence is impossible in the standard J₁ Skorokhod topology. In joint work with Roland Zweimüller, we prove convergence to the Lévy process in the slightly weaker M₁ topology.

(This talk will not assume any familiarity with J₁ or M₁ Skorokhod topologies!)