688 citations · 2.4k across the 52 of their papers we have counts for
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Variance continuity for Lorenz flows
Wael Bahsoun, Ian Melbourne, Marks Ruziboev
The classical Lorenz flow, and any flow which is close to it in the -topology, satisfies a Central Limit Theorem (CLT). We prove that the variance in the CLT varies continuous…
Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards
Henk Bruin, Ian Melbourne, Dalia Terhesiu
Gouezel and Sarig introduced operator renewal theory as a method to prove sharp results on polynomial decay of correlations for certain classes of nonuniformly expanding maps. In t…
Convergence to a Lévy process in the Skorohod and topologies for nonuniformly hyperbolic systems, including billiards with cusps
Ian Melbourne, Paulo Varandas
We prove convergence to a Levy process for a class of dispersing billiards with cusps. For such examples, convergence to a stable law was proved by Jung & Zhang. For the correspond…
Rate of Convergence in the Weak Invariance Principle for Deterministic Systems
Marios Antoniou, Ian Melbourne
We obtain the first results on convergence rates in the Prokhorov metric for the weak invariance principle (functional central limit theorem) for deterministic dynamical systems. O…
Statistical properties for flows with unbounded roof function, including the Lorenz attractor
Peter Balint, Ian Melbourne
For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general…