688 citations · 2.4k across the 52 of their papers we have counts for
59 papers
Good inducing schemes for uniformly hyperbolic flows, and applications to exponential decay of correlations
Ian Melbourne, Paulo Varandas
Given an Axiom A attractor for a flow (), we construct a countable Markov extension with exponential return times in such a way that the inducing set is a smoothly e…
Time-reversibility and nonvanishing Levy area
Georg Gottwald, Ian Melbourne
We give a complete description and clarification of the structure of the Levy area correction to Ito/Stratonovich stochastic integrals arising as limits of time-reversible determin…
Local large deviations for periodic infinite horizon Lorentz gases
Ian Melbourne, Francoise Pene, Dalia Terhesiu
We prove local large deviations for the periodic infinite horizon Lorentz gas viewed as a -cover () of a dispersing billiard. In addition to this specific exa…
Polynomial decay of correlations for nonpositively curved surfaces
Yuri Lima, Carlos Matheus, Ian Melbourne
We prove polynomial decay of correlations for geodesic flows on a class of nonpositively curved surfaces where zero curvature only occurs along one closed geodesic. We also prove t…
Nonexistence of spectral gaps in Hölder spaces for continuous time dynamical systems
Ian Melbourne, Nicolo Paviato, Dalia Terhesiu
We show that there is a natural restriction on the smoothness of spaces where the transfer operator for a continuous dynamical system has a spectral gap. Such a space cannot be emb…
Decay in norm of transfer operators for semiflows
Ian Melbourne, Nicolo Paviato, Dalia Terhesiu
We establish exponential decay in Hölder norm of transfer operators applied to smooth observables of uniformly and nonuniformly expanding semiflows with exponential decay of correl…