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Mosc. Math. J., 2005, Volume 5, Number 3, Pages 537–576 (Mi mmj210)  

This article is cited in 19 scientific papers (total in 19 papers)

Averaging and invariant measures

D. I. Dolgopyat

University of Maryland

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.


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MSC: Primary 34C29; Secondary 37D30
Received: May 12, 2005; in revised form August 9, 2005

Citation: D. I. Dolgopyat, “Averaging and invariant measures”, Mosc. Math. J., 5:3 (2005), 537–576

Citation in format AMSBIB
\by D.~I.~Dolgopyat
\paper Averaging and invariant measures
\jour Mosc. Math.~J.
\yr 2005
\vol 5
\issue 3
\pages 537--576

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    This publication is cited in the following articles:
    1. Dolgopyat D., “Bouncing balls in non-linear potentials”, Discrete Contin. Dyn. Syst., 22:1-2 (2008), 165–182  crossref  mathscinet  zmath  isi
    2. Burns K., Dolgopyat D., Pesin Ya., Pollicott M., “Stable ergodicity for partially hyperbolic attractors with negative central exponents”, J. Mod. Dyn., 2:1 (2008), 63–81  crossref  mathscinet  zmath  isi
    3. Bakhtin V., Kifer Yu., “Nonconvergence examples in averaging”, Geometric and Probabilistic Structures in Dynamics, Contemporary Mathematics Series, 469, 2008, 1–17  crossref  mathscinet  isi
    4. Dolgopyat D., “Fermi acceleration”, Geometric and Probabilistic Structures in Dynamics, Contemporary Mathematics Series, 469, 2008, 149–166  crossref  mathscinet  zmath  isi
    5. Brännstrom N., “Averaging in weakly coupled discrete dynamical systems”, J. Nonlinear Math. Phys., 16:4 (2009), 465–487  crossref  mathscinet  zmath  isi  elib  scopus
    6. Kifer Yu., Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging, Mem. Amer. Math. Soc., 201, no. 944, 2009, viii+129 pp.  mathscinet  isi
    7. Chernov N., Dolgopyat D., “The Galton board: limit theorems and recurrence”, J. Amer. Math. Soc., 22:3 (2009), 821–858  crossref  mathscinet  zmath  isi  scopus
    8. Liverani C., “On the work and vision of Dmitry Dolgopyat”, J. Mod. Dyn., 4:2 (2010), 211–225  crossref  mathscinet  zmath  isi  scopus
    9. Pesin Ya., “On the work of Dolgopyat on partial and nonuniform hyperbolicity”, J. Mod. Dyn., 4:2 (2010), 227–241  crossref  mathscinet  zmath  isi  elib  scopus
    10. Melbourne I., Stuart A.M., “A note on diffusion limits of chaotic skew-product flows”, Nonlinearity, 24:4 (2011), 1361–1367  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Dolgopyat D., Liverani C., “Energy Transfer in a Fast-Slow Hamiltonian System”, Comm Math Phys, 308:1 (2011), 201–225  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Kifer Yu., “Nonconventional Limit Theorems in Averaging”, Ann. Inst. Henri Poincare-Probab. Stat., 50:1 (2014), 236–255  crossref  mathscinet  zmath  isi  scopus
    13. Kelly D., Melbourne I., “Smooth Approximation of Stochastic Differential Equations”, Ann. Probab., 44:1 (2016), 479–520  crossref  mathscinet  zmath  isi  scopus
    14. De Simoi J., Liverani C., “Statistical Properties of Mostly Contracting Fast-Slow Partially Hyperbolic Systems”, Invent. Math., 206:1 (2016), 147–227  crossref  mathscinet  zmath  isi  scopus
    15. Kelly D., Melbourne I., “Deterministic Homogenization For Fast Slow Systems With Chaotic Noise”, J. Funct. Anal., 272:10 (2017), 4063–4102  crossref  mathscinet  zmath  isi  scopus
    16. Dobbs N., Stenlund M., “Quasistatic Dynamical Systems”, Ergod. Theory Dyn. Syst., 37:8 (2017), 2556–2596  crossref  zmath  isi  scopus
    17. 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  crossref  zmath  isi  scopus
    18. De Simoi J., Liverani C., “Limit Theorems For Fast-Slow Partially Hyperbolic Systems”, Invent. Math., 213:3 (2018), 811–1016  crossref  mathscinet  zmath  isi  scopus
    19. 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  crossref  mathscinet  zmath  isi  scopus
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