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Number of items: 61.

Journal Article

Korepanov, Alexey, Kosloff, Zemer and Melbourne, Ian (2022) Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1. Annales de l'Institut Henri PoincarΓ© (B) ProbabilitΓ©s et Statistiques, 58 (3). pp. 1305-1327. doi:10.1214/21-AIHP1202 ISSN 0246-0203.

Chevyrev, Ilya, Friz, Peter, Korepanov, Alexey, Melbourne, Ian and Zhang, Huilin (2022) Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2. Annales de l'Institut Henri PoincarΓ© (B) ProbabilitΓ©s et Statistiques, 58 (3). 1328-1350 . doi:10.1214/21-AIHP1203 ISSN 0246-0203.

Galton, Matt and Melbourne, Ian (2022) Iterated invariance principle for slowly mixing dynamical systems. Annales de l'Institut Henri Poincare (B) Probability and Statistics, 58 (2). pp. 1284-1304. doi:10.1214/21-AIHP1190 ISSN 0246-0203.

Melbourne, Ian, Paviato, Nicolo and Terhesiu, Dalia (2022) Nonexistence of spectral gaps in HΓΆlder spaces for continuous time dynamical systems. Israel Journal of Mathematics, 247 . pp. 987-991. doi:10.1007/s11856-021-2273-3 ISSN 0021-2172.

Melbourne, Ian and Terhesiu, Dalia (2022) Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems. Electronic Journal of Probability, 27 . 21. doi:10.1214/22-EJP750 ISSN 1083-6489.

Melbourne, Ian, Paviato, Nicolo and Terhesiu, Dalia (2022) Decay in norm of transfer operators for semiflows. Studia Mathematica, 266 . pp. 149-166. doi:10.4064/sm210410-7-3 ISSN 0039-3223.

Melbourne, Ian, Pene, Francoise and Terhesiu, Dalia (2022) Local large deviations for periodic infinite horizon Lorentz gases. Journal d'Analyse Mathematique . ISSN 0021-7670. (In Press)

Eslami, Peyman, Melbourne, Ian and Vaienti, Sandro (2021) Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps. Advances in Mathematics, 388 . 107853. doi:10.1016/j.aim.2021.107853 ISSN 0001-8708.

Jung, Paul, Melbourne, Ian, Pene, Francoise, Varandas, Paulo and Zhang, Hong-Kun (2021) Necessary and sufficient condition for M2-convergence to a LΓ©vy process for billiards with cusps at flat points. Stochastics and Dynamics, 21 (5). 2150024. doi:10.1142/S0219493721500246 ISSN 0219-4937.

Bruin, Henk, Melbourne, Ian and Terhesiu, Dalia (2021) Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards. Annales Henri Lebesgue, 4 . pp. 407-451. doi:10.5802/ahl.76

Gottwald, Georg A. and Melbourne, Ian (2021) Simulation of non-lipschitz stochastic differential 2 equations driven by Ξ±-stable noise : a method based on deterministic homogenisation. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 19 (2). pp. 665-687. doi:10.1137/20M1333183 ISSN 1540-3459.

Chevyrev, Ilya, Friz, Peter K., Korepanov, Alexey and Melbourne, Ian (2020) Superdiffusive limits for deterministic fast–slow dynamical systems. Probability Theory and Related Fields, 178 . pp. 735-770. doi:10.1007/s00440-020-00988-5 ISSN 0178-8051.

Demers, Mark, Melbourne, Ian and Nicol, Matthew (2020) Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas. Nonlinearity, 33 (8). 4095. doi:10.1088/1361-6544/ab7d22 ISSN 0951-7715.

Bahsoun, Wael, Melbourne, Ian and Ruziboev, Marks (2020) Variance continuity for Lorenz flows. Annales Henri Poincare, 21 . pp. 1873-1892. doi:10.1007/s00023-020-00913-5 ISSN 1424-0637.

Melbourne, Ian and Varandas, Paulo (2020) Convergence to a LΓ©vy process in the Skorohod M1 and M2 topologies for nonuniformly hyperbolic systems, including billiards with cusps. Communications in Mathematical Physics, 375 . pp. 653-678. doi:10.1007/s00220-019-03501-9 ISSN 0010-3616.

Melbourne, Ian and Terhesiu, Dalia (2020) Renewal theorems and mixing for non Markov flows with infinite measure. Annales de l'Institut Henri PoincarΓ© (B) ProbabilitΓ©s et Statistiques, 56 (1). pp. 449-476. doi:10.1214/19-AIHP968 ISSN 0246-0203.

Antoniou, Marios and Melbourne, Ian (2019) Rate of Convergence in the Weak Invariance Principle for Deterministic Systems. Communications in Mathematical Physics, 369 (3). pp. 1147-1165. doi:10.1007/s00220-019-03334-6 ISSN 0010-3616.

AraΓΊjo, V. and Melbourne, Ian (2019) Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation. Advances in Mathematics, 349 . pp. 212-245. doi:10.1016/j.aim.2019.04.007 ISSN 0001-8708.

BΓ‘lint, PΓ©ter, Butterley, Oliver and Melbourne, Ian (2019) Polynomial decay of correlations for flows, including Lorentz gas examples. Communications in Mathematical Physics, 368 (1). pp. 55-111. doi:10.1007/s00220-019-03423-6 ISSN 0010-3616.

Korepanov, A., Kosloff, Z. and Melbourne, I. (2019) Explicit coupling argument for non-uniformly hyperbolic transformations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 149 (1). pp. 101-130. doi:10.1017/S0308210518000161 ISSN 0308-2105.

Korepanov, Alexey, Kosloff, Zemer and Melbourne, Ian (2019) Explicit coupling argument for nonuniformly hyperbolic transformations. Proceedings of the Royal Society of Edinburgh Section A : Mathematics, 149 (1). pp. 101-130. doi:10.1017/S0308210518000161 ISSN 0308-2105.

Antoniou, Marios and Melbourne, Ian (2019) Rate of convergence in the weak invariance principle for deterministic systems. Communications in Mathematical Physics, 369 . pp. 1147-1165. doi:10.1007/s00220-019-03334-6 ISSN 0010-3616.

Bruin, Henk, Melbourne, Ian and Terhesiu, Dalia (2019) Rates of mixing for non-Markov infinite measure semiflows. Transactions of the American Mathematical Society, 371 . pp. 7343-7386. doi:10.1090/tran/7582 ISSN 0002-9947.

Melbourne, Ian and Terhesiu, Dalia (2018) Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure. Journal of Modern Dynamics, 12 . pp. 285-313. doi:10.3934/jmd.2018011 ISSN 1930-5311.

Bruin, Henk, Melbourne, Ian and Terhesiu, Dalia (2018) Rates of mixing for non-Markov infinite measure semiflows. Transactions of the American Mathematical Society, 371 (10). pp. 7343-7386. doi:10.1090/tran/7582 ISSN 0002-9947.

Melbourne, Ian (2018) Superpolynomial and polynomial mixing for semiflows and flows. Nonlinearity, 31 (10). R268. doi:10.1088/1361-6544/aad309 ISSN 0951-7715.

BΓ‘lint, PΓ©ter and Melbourne, Ian (2018) Statistical properties for flows with unbounded roof function, including the Lorenz attractor. Journal of Statistical Physics, 172 (4). pp. 1101-1126. doi:10.1007/s10955-018-2093-y ISSN 0022-4715.

Korepanov, Alexey, Kosloff, Zemer and Melbourne, Ian (2018) Martingale-coboundary decomposition for families of dynamical systems. Annales de l'Institut Henri Poincare (C) Non Linear Analysis , 35 (4). pp. 859-885. doi:10.1016/j.anihpc.2017.08.005 ISSN 0294-1449.

Kelly, David and Melbourne, Ian (2017) Deterministic homogenization for fast-slow systems with chaotic noise. Journal of Functional Analysis, 272 (10). pp. 4063-4102. doi:10.1016/j.jfa.2017.01.015 ISSN 0022-1236.

Korepanov, Alexey, Kosloff, Zemer and Melbourne, Ian (2017) Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems. Studia Mathematica, 238 . pp. 59-89. doi:10.4064/sm8540-1-2017 ISSN 0039-3223.

AraΓΊjo, Vitor and Melbourne, Ian (2017) Existence and smoothness of the stable foliation for sectional hyperbolic attractors. Bulletin of the London Mathematical Society, 49 (2). pp. 351-367. doi:10.1112/blms.12037 ISSN 0024-6093 .

Melbourne, Ian and Terhesiu, Dalia (2017) Operator renewal theory for continuous time dynamical systems with finite and infinite measure. Monatshefte fur Mathematik, 182 (2). pp. 377-431. doi:10.1007/s00605-016-0922-0 ISSN 0026-9255.

Butterley, Oliver and Melbourne, Ian (2017) Disintegration of invariant measures for hyperbolic skew products. Israel Journal of Mathematics, 219 (1). pp. 171-188. doi:10.1007/s11856-017-1477-z ISSN 0021-2172.

Gottwald, Georg A. and Melbourne, Ian (2016) On the detection of superdiffusive behaviour in time series. Journal of Statistical Mechanics: Theory and Experiment, 2016 . 123205. doi:10.1088/1742-5468/aa4f0f ISSN 1742-5468.

AraΓΊjo, Vitor and Melbourne, Ian (2016) Exponential decay of correlations for nonuniformly hyperbolic flows with a C1+Ξ±C1+Ξ± stable foliation, including the classical Lorenz attractor. Annales Henri PoincarΓ©, 17 (11). pp. 2975-3004. doi:10.1007/s00023-016-0482-9 ISSN 1424-0637.

Gottwald, Georg A. and Melbourne, Ian (2016) Central limit theorems and suppression of anomalous diffusion for systems with symmetry. Nonlinearity, 29 (10). 2941. doi:10.1088/0951-7715/29/10/2941 ISSN 0951-7715.

Gottwald, Georg A. and Melbourne, Ian (2016) Broadband nature of power spectra for intermittent maps with summable and nonsummable decay of correlations. Journal of Physics A: Mathematical and Theoretical, 49 (17). 174003. doi:10.1088/1751-8113/49/17/174003 ISSN 1751-8113.

Melbourne, Ian and Varandas, Paulo (2016) A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansion. Stochastics and Dynamics, 16 (03). 1660012. doi:10.1142/S0219493716600121 ISSN 0219-4937.

Kelly, David and Melbourne, Ian (2016) Smooth approximation of stochastic differential equations. The Annals of Probability, 44 (1). pp. 479-520. doi:10.1214/14-AOP979 ISSN 0091-1798.

Melbourne, Ian and Terhesiu, Dalia (2014) Decay of correlations for non-uniformly expanding systems with general return times. Ergodic Theory and Dynamical Systems, Volume 34 (Number 6). pp. 893-918. doi:10.1017/etds.2012.158 ISSN 0143-3857.

GouΓ«zel, SΓ©bastien and Melbourne, Ian (2014) Moment bounds and concentration inequalities for slowly mixing dynamical systems. Electronic Journal of Probability, 19 . pp. 1-30. doi:10.1214/EJP.v19-3427 ISSN 1083-6489.

Gottwald, Georg A. and Melbourne, Ian (2014) A test for a conjecture on the nature of attractors for smooth dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 24 (Number 2). Article number 024403. doi:10.1063/1.4868984 ISSN 1054-1500.

Gottwald, G. A. and Melbourne, Ian (2013) Homogenization for deterministic maps and multiplicative noise. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 469 (Number 2156). Article number 20130201. doi:10.1098/rspa.2013.0201 ISSN 1364-5021.

Melbourne, Ian and Terhesiu, Dalia (2013) First and higher order uniform dual ergodic theorems for dynamical systems with infinite measure. Israel Journal of Mathematics, Volume 194 (Number 2). pp. 793-830. doi:10.1007/s11856-012-0154-5 ISSN 0021-2172.

Gottwald, G. A. and Melbourne, Ian (2013) A Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Proceedings of the National Academy of Sciences of the United States of America, Volume 110 (Number 21). pp. 8411-8416. doi:10.1073/pnas.1217926110 ISSN 0027-8424.

Luzzatto, Stefano and Melbourne, Ian (2013) Statistical properties and decay of correlations for interval maps with critical points and singularities. Communications in Mathematical Physics, Volume 320 (Number 1). pp. 21-35. doi:10.1007/s00220-013-1709-y ISSN 0010-3616.

Melbourne, Ian and Torok, Andrei (2012) Convergence of moments for Axiom A and non-uniformly hyperbolic flows. Ergodic Theory and Dynamical Systems, Vol.32 (No.3). pp. 1091-1100. doi:10.1017/S0143385711000174 ISSN 0143-3857.

Melbourne, Ian and Terhesiu, Dalia (2012) Operator renewal theory and mixing rates for dynamical systems with infinite measure. Inventiones mathematicae, Vol. 189 (No. 1). pp. 61-110. doi:10.1007/s00222-011-0361-4 ISSN 0020-9910.

Melbourne, Ian, Nijica, Viorel and Torok, Andrei (2012) Transitivity of Heisenberg group extensions of hyperbolic systems. Ergodic Theory and Dynamical Systems, Vol.32 (No.1). pp. 223-235. doi:10.1017/S014338571000091X ISSN 0143-3857.

Melbourne, Ian and Stuart, A. M. (2011) A note on diffusion limits of chaotic skew-product flows. Nonlinearity, Volume 24 (Number 4). pp. 1361-1367. doi:10.1088/0951-7715/24/4/018 ISSN 0951-7715.

Bruin, Henk, Demers, Mark and Melbourne, Ian (2010) Existence and convergence properties of physical measures for certain dynamical systems with holes. Ergodic Theory and Dynamical Systems, Vol.30 (No.3). pp. 687-728. doi:10.1017/S0143385709000200 ISSN 0143-3857.

Gottwald, Georg A. and Melbourne, Ian (2009) On the implementation of the 0–1 test for chaos. SIAM Journal on Applied Dynamical Systems, Vol.8 (No.1). pp. 129-145. doi:10.1137/080718851 ISSN 1536-0040.

Gottwald, Georg A. and Melbourne, Ian (2009) On the validity of the 0–1 test for chaos. Nonlinearity, Vol.22 (No.6). pp. 1367-1382. doi:10.1088/0951-7715/22/6/006 ISSN 0951-7715.

Melbourne, Ian, Nitica, V. and Torok, Andrei (2009) Transitivity of Euclidean-type extensions of hyperbolic systems. Ergodic Theory and Dynamical Systems, Vol.29 (No.5). pp. 1585-1602. doi:10.1017/S0143385708000886 ISSN 0143-3857.

Melbourne, Ian and Nicol, Matthew (2009) A vector-valued almost sure invariance principle for hyperbolic dynamical systems. The Annals of Probability, Vol.37 (No.2). pp. 478-505. doi:10.1214/08-AOP410 ISSN 0091-1798.

Gottwald, Georg A. and Melbourne, Ian (2008) Comment on β€œReliability of the 0-1 test for chaos”. Physical Review E, Vol.77 (No.2). Article no. 028201 . doi:10.1103/PhysRevE.77.028201 ISSN 1539-3755.

BΓ‘lint, PΓ©ter and Melbourne, Ian (2008) Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows. Journal of Statistical Physics, Vol.133 (No.3). pp. 435-447. doi:10.1007/s10955-008-9623-y ISSN 0022-4715.

Melbourne, Ian (2008) Decay of correlations for slowly mixing flows. Proceedings of the London Mathematical Society, Vol. 98 (No. 1). pp. 163-190. doi:10.1112/plms/pdn028 ISSN 0024-6115.

Melbourne, Ian (2008) Large and moderate deviations for slowly mixing dynamical systems. Proceedings of the American Mathematical Society, Vol.137 (No.5). pp. 1735-1741. doi:10.1090/S0002-9939-08-09751-7 ISSN 0002-9939.

Melbourne, Ian and Nicol, Matthew (2008) Large deviations for nonuniformly hyperbolic systems. Transactions of the American Mathematical Society, Vol.360 (No.12). pp. 6661-6676. doi:10.1090/S0002-9947-08-04520-0 ISSN 0002-9947.

Melbourne, Ian and Gottwald, Georg A (2008) Power spectra for deterministic chaotic dynamical systems. Nonlinearity, vol.21 (No.1). pp. 179-189. doi:10.1088/0951-7715/21/1/010 ISSN 0951-7715.

This list was generated on Tue Mar 21 21:56:54 2023 GMT.