Ian Melbourne

Mathematics · Physical Sciences

38h-index5.8kcitations192works0.92yr avg
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Research Topics

Mathematical Dynamics and Fractals(120), Quantum chaos and dynamical systems(85), Nonlinear Dynamics and Pattern Formation(52), Stochastic processes and statistical mechanics(38), Chaos control and synchronization(27)

Publications192 total

Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows
arXiv (Cornell University)·2025Open Access
Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia
ArXiv.org·2025Open Access
Global-local mixing for infinite measure dynamical systems
arXiv (Cornell University)·2025Open Access
Superdiffusive limits beyond the Marcus regime for deterministic fast-slow systems
Communications of the American Mathematical Society·2024· 2 citedOpen Access
Natural measures and statistical properties of non-statistical maps with multiple neutral fixed points
arXiv (Cornell University)·2024Open Access
Time-reversibility and nonvanishing Lévy area
Nonlinearity·2024· 1 citedOpen Access
Good Inducing Schemes for Uniformly Hyperbolic Flows, and Applications to Exponential Decay of Correlations
Annales Henri Poincaré·2024· 2 citedOpen Access
Polynomial decay of correlations for nonpositively curved surfaces
Transactions of the American Mathematical Society·2024· 2 citedOpen Access
Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems
Electronic Journal of Probability·2024· 1 citedOpen Access
Superdiffusive limits beyond the Marcus regime for deterministic fast-slow systems
arXiv (Cornell University)·2023· 1 citedOpen Access
Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems
arXiv (Cornell University)·2023Open Access
Local large deviations for periodic infinite horizon Lorentz gases
Journal d Analyse Mathématique·2023· 4 citedOpen Access
Good inducing schemes for uniformly hyperbolic flows, and applications to exponential decay of correlations
arXiv (Cornell University)·2023Open Access
Time-reversibility and nonvanishing Levy area
arXiv (Cornell University)·2022· 1 citedOpen Access
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1
Annales de l Institut Henri Poincaré Probabilités et Statistiques·2022· 11 cited
Deterministic homogenization under optimal moment assumptions for fast–slow systems. Part 2
Annales de l Institut Henri Poincaré Probabilités et Statistiques·2022· 7 cited
Iterated invariance principle for slowly mixing dynamical systems
Annales de l Institut Henri Poincaré Probabilités et Statistiques·2022· 1 cited
ETS volume 42 issue 2 Cover and Back matter
Ergodic Theory and Dynamical Systems·2022Open Access
Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems
Electronic Journal of Probability·2022· 15 citedOpen Access
Decay in norm of transfer operators for semiflows
Studia Mathematica·2022
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Frequent Co-authors

Georg A. Gottwald(9), Matthew Nicol(6), Martin Golubitsky(4), Martin Krupa(3), Pascal Chossat(3), Andrei Török(3), Michael Field(3), Peter Ashwin(3), David Kelly(2), Michael Dellnitz(2), Victor G. LeBlanc(2), Dalia Terhesiu(2), Alexey Korepanov(2), Jeroen S.W. Lamb(2), Ian R. Falconer(1), Kjetil Wormnes(1), Reiner Lauterbach(1), Andrew M. Stuart(1), Mark Holland(1), Andrew Török(1)