688 citations · 2.4k across the 52 of their papers we have counts for
5 papers · 1 filter
A test for a conjecture on the nature of attractors for smooth dynamical systems
Georg A. Gottwald, Ian Melbourne
Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonunif…
Weak Convergence to Stable Lévy Processes for Nonuniformly Hyperbolic Dynamical Systems
Ian Melbourne, Roland Zweimüller
We consider weak invariance principles (functional limit theorems) in the domain of a stable law. A general result is obtained on lifting such limit laws from an induced dynamical…
Mixing for continuous time dynamical systems with infinite measure
Ian Melbourne, Dalia Terhesiu
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. E…
A Huygens principle for diffusion and anomalous diffusion in spatially extended systems
Georg A. Gottwald, Ian Melbourne
We present a universal view on diffusive behaviour in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusi…
Homogenization for Deterministic Maps and Multiplicative Noise
Georg A. Gottwald, Ian Melbourne
A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-sl…