688 citations · 2.4k across the 52 of their papers we have counts for
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Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure
Ian Melbourne, Dalia Terhesiu
We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure sett…
Broadband nature of power spectra for intermittent Maps with summable and nonsummable decay of correlations
Georg A. Gottwald, Ian Melbourne
We present results on the broadband nature of the power spectrum , , for a large class of nonuniformly expanding maps with summable and nonsummable decay of corre…
Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems
A. Korepanov, Z. Kosloff, I. Melbourne
We consider families of fast-slow skew product maps of the form \begin{align*} x_{n+1} = x_n+εa(x_n,y_n,ε), \quad y_{n+1} = T_εy_n, \end{align*} where is a family of nonunifo…
Exponential decay of correlations for nonuniformly hyperbolic flows with a C^{1+α} stable foliation, including the classical Lorenz attractor
Vitor Araújo, Ian Melbourne
We prove exponential decay of correlations for a class of uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular, this es…
Disintegration of Invariant Measures for Hyperbolic Skew Products
Oliver Butterley, Ian Melbourne
We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from…