688 citations · 2.4k across the 52 of their papers we have counts for
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math.DS2006★ 24 cited
Decay of correlations for slowly mixing flows
Ian Melbourne
We show that polynomial decay of correlations is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of a class of nonuniformly hyp…
nlin.PS2006
Dynamics on unbounded domains; co-solutions and inheritance of stability
Peter Ashwin, Ian Melbourne
We consider the dynamics of semiflows of patterns on unbounded domains that are equivariant under a noncompact group action. We exploit the unbounded nature of the domain in a sett…
math.DS2006★ 3 cited
A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical Systems
Ian Melbourne, Matthew Nicol
We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynam…