Publications by topic (under construction):
Fast-slow systems: homogenisation, averaging, interpretation of stochastic integrals, rough path theory, Lévy area, iterated invariance principle Anomalous diffusion: convergence to α-stable processes and Lévy processes, M1 and M2 Skorokhod topology, non-Skorokhod topologies, decorated càdlàg spaces Lorenz attractor: classical Lorenz attractor has exponential decay of correlations; smoothness of stable foliation; singular hyperbolic attractors; statistical properties Rates of mixing for (nonuniformly) hyperbolic flows: exponential mixing, rapid mixing, polynomial mixing Rates of mixing and statistical limit laws for dispersing billiards and Lorentz flows: dispersing billiard flows with cusps and externally forced dispersing billiard flows are rapid mixing; infinite horizon Lorentz gas mixes at rate 1/t; sharp lower bounds for slowly mixing dispersing billiards Infinite ergodic theory: Krickeberg mixing, global-local mixing; operator renewal theory, natural measures Statistical limit laws (excluding stable laws/Lévy processes): central limit theorem, invariance principles, moments, large deviations Stable transitivity Rn extensions, Euclidean extensions, Heisenberg group; stable ergodicity, stable mixing