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!)
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