688 citations · 2.4k across the 52 of their papers we have counts for
5 papers · 2 filters
Multiscale systems, homogenization, and rough paths
Ilya Chevyrev, Peter K. Friz, Alexey Korepanov +2
In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classi…
Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation
Vitor Araujo, Ian Melbourne
Over the last 10 years or so, advanced statistical properties, including exponential decay of correlations, have been established for certain classes of singular hyperbolic flows i…
Polynomial decay of correlations for flows, including Lorentz gas examples
Peter Balint, Oliver Butterley, Ian Melbourne
We prove sharp results on polynomial decay of correlations for nonuniformly hyperbolic flows. Applications include intermittent solenoidal flows and various Lorentz gas models incl…
Superpolynomial and polynomial mixing for semiflows and flows
Ian Melbourne
We give a review of results on superpolynomial decay of correlations, and polynomial decay of correlations for nonuniformly expanding semiflows and nonuniformly hyperbolic flows. A…
Renewal theorems and mixing for non Markov flows with infinite measure
Ian Melbourne, Dalia Terhesiu
We obtain results on mixing for a large class of (not necessarily Markov) infinite measure semiflows and flows. Erickson proved, amongst other things, a strong renewal theorem in t…