Professor Ian Melbourne
Professor of Mathematics
Teaching Responsibilities 2018/19:
Term 1: MA433 Fourier Analysis
Term 2: MA427 Ergodic Theory
Research Interests: Ergodic theory and dynamical systems. Links with stochastic analysis.
ICM Brazil 2018. Satellite Conference: Dynamical systems and related topics. Salvador, Bahia, Brasil, 13 to 17 August 2018.
Organizers: C. Bonatti, L. Diaz, M. Lyubich, I. Melbourne, C. Moreira and M. J. Pacifico.
Workshop at CIRM, Luminy, 2018. Probabilistic Limit Theorems for Dynamical Systems (Théorèmes limites probabilistes pour les systèmes dynamiques):. Marseille, France, 29 October to 2 November 2018.
Organizers: I. Melbourne, F. Pène and D. Volny.
Selected recent publications:
D. Kelly and I. Melbourne. Smooth approximation of stochastic differential equations. Annals of Probability 44 (2016) 479-520.
G. A. Gottwald and I. Melbourne. A Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Proc. Natl. Acad. Sci. USA 110 (2013) 8411-8416.
I. Melbourne and D. Terhesiu. Operator renewal theory and mixing rates for dynamical systems with infinite measure. Inventiones Mathematicae 189 (2012) 61-110.
I. Melbourne and M. Nicol. A vector-valued almost sure invariance principle for hyperbolic dynamical systems. Annals of Probability 37 (2009) 478-505.
I. Melbourne. Decay of correlations for slowly mixing flows. Proc. London Math. Soc. 98 (2009) 163-190.
M. Field, I. Melbourne and A. Török. Stability of mixing and rapid mixing for hyperbolic flows. Annals of Math. 166 (2007) 269-291.