Abstract:
An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along the leaves of this foliation. We review recent results on this subject and present some extensions and open questions.
Key words and phrases:
Averaging, Sinai–Ruelle–Bowen measures, partial hyperbolicity, decay of correlations.
Received:May 12, 2005; in revised form August 9, 2005
This publication is cited in the following 33 articles:
Ilya Chevyrev, Alexey Korepanov, Ian Melbourne, “Superdiffusive limits beyond the Marcus regime for deterministic fast-slow systems”, Comm. Amer. Math. Soc., 4:16 (2024), 746
Fabrizio Lillo, Giulia Livieri, Stefano Marmi, Anton Solomko, Sandro Vaienti, “Unimodal Maps Perturbed by Heteroscedastic Noise: An Application to a Financial Systems”, J Stat Phys, 190:10 (2023)
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Mark F. Demers, Carlangelo Liverani, “Projective Cones for Sequential Dispersing Billiards”, Commun. Math. Phys., 401:1 (2023), 841
Matt Galton, Ian Melbourne, “Iterated invariance principle for slowly mixing dynamical systems”, Ann. Inst. H. Poincaré Probab. Statist., 58:2 (2022)
Alexey Korepanov, Zemer Kosloff, Ian Melbourne, “Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1”, Ann. Inst. H. Poincaré Probab. Statist., 58:3 (2022)
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Pablo D. Carrasco, “Random Products of Standard Maps”, Commun. Math. Phys., 377:2 (2020), 773
Ilya Chevyrev, Peter K. Friz, Alexey Korepanov, Ian Melbourne, “Superdiffusive limits for deterministic fast–slow dynamical systems”, Probab. Theory Relat. Fields, 178:3-4 (2020), 735
Grigo A., “a Rigorous Derivation of Haff'S Law For a Periodic Two-Disk Fluid”, J. Stat. Phys., 176:4 (2019), 806–835
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Wouters J., Gottwald G.A., “Edgeworth Expansions For Slow-Fast Systems With Finite Time-Scale Separation”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 475:2223 (2019), 20180358
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Balint P., Nandori P., Szasz D., Toth I.P., “Equidistribution For Standard Pairs in Planar Dispersing Billiard Flows”, Ann. Henri Poincare, 19:4 (2018), 979–1042
Kelly D., Melbourne I., “Deterministic Homogenization For Fast Slow Systems With Chaotic Noise”, J. Funct. Anal., 272:10 (2017), 4063–4102
Dobbs N., Stenlund M., “Quasistatic Dynamical Systems”, Ergod. Theory Dyn. Syst., 37:8 (2017), 2556–2596
Korepanov A., Melbourne I., Kosloff Z., “Averaging and Rates of Averaging For Uniform Families of Deterministic Fast-Slow Skew Product System”, Studia Math., 238:1 (2017), 59–89
Kelly D., Melbourne I., “Smooth Approximation of Stochastic Differential Equations”, Ann. Probab., 44:1 (2016), 479–520
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