688 citations · 2.4k across the 52 of their papers we have counts for
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Decay of correlations for nonuniformly expanding systems with general return times
Ian Melbourne, Dalia Terhesiu
We give a unified treatment of decay of correlations for nonuniformly expanding systems with a good inducing scheme. In addition to being more elementary than previous treatments,…
Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities
Stefano Luzzatto, Ian Melbourne
We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the gr…
First and higher order uniform dual ergodic theorems for dynamical systems with infinite measure
Ian Melbourne, Dalia Terhesiu
We generalize the proof of Karamata's Theorem by the method of approximation by polynomials to the operator case. As a consequence, we offer a simple proof of \emph{uniform dual er…
A Note on Diffusion Limits of Chaotic Skew Product Flows
I. Melbourne, A. M. Stuart
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assu…