Limit theorems for partially hyperbolic systems

By Dmitry Dolgopyat. 2003

247 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0e514fec2c9c66441eb863aaa93d96e19eec7b39

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Ian Melbourne
2. S. Gouëzel
3. David Kelly
4. Zemer Kosloff
5. A. Korepanov
6. Andrei Török
7. N. Haydn
8. Yakov Pesin

In Statistical and Nonlinear Physics

1. Ian Melbourne
2. S. Gouëzel
3. David Kelly
4. N. Haydn
5. Zemer Kosloff
6. A. Korepanov
7. Andrei Török
8. Yakov Pesin

Citations in the corpus

• On circle rotations and the shrinking target properties (2007, background): “Expanding maps of the circle [10] and Anosov diffeomorphisms [3], for example, have STP.”
• Averaging and Invariant Measures (2005, unknown): “In this note we review recent results about statistical properties and stability of SRB measures [18], [19] and then show how the methods of the these two papers can be combined to obtain new results in this area.”
• Berry-Esseen theorem and local limit theorem for non uniformly expanding maps (2003, methodology): “Among many techniques, the most flexible one is probably the martingale argument of Gordin (see for example [23,26,10,11,36]).”
• Statistical limit theorems for suspension flows (2004, background): “Usually the dynamical system X is assumed to have some hyperbolicity properties (Axiom A or nonuniformly/partially hyperbolic, see for example [25, 27, 30, 31, 7, 11, 22]) or expansivity properties (for example [28, 19]), and the observation Φ is assumed to have certain regularity properties such as”
• Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence (2009, background): “This kind of problem is also connected with the so called dynamical Borel Cantelli results (see [17] and e.g. [41, 20, 17, 13 ]).”
• Martingale–coboundary decomposition for families of dynamical systems (2016, methodology): “When the fast dynamics Tǫ is independent of ǫ, the corresponding result without exactness is proved for partially hyperbolic dynamics using standard pairs/martingale problems [24], and for nonuniformly hyperbolic dynamics using rough path theory [33, 34].”
• Logarithm laws for unipotent flows, I (2008, background): “There are many results on STP’s for hyperbolic ([4, 5, 8, 11]) and elliptic ([6, 16]) systems, but it would be interesting to obtain more results for parabolic systems like unipotent flows.”
• On mixing properties of compact group extensions of hyperbolic systems (2002, unknown): “More applications will be presented elsewhere [ 23 ].”
• Smooth approximation of stochastic differential equations (2014, methodology): “MR2034323 [15] Dolgopyat, D. (2005).”
• Mixing in the Absence of the Shrinking Target Property (2006, background): “It has been proved, for example, that expanding maps of the circle [11] and Anosov diffeomorphisms on topological spaces [3] have the shrinking target property.”
• On differentiability of SRB states for partially hyperbolic systems (2004, background): “Proposition 2.1. ([ 22 ], Proposition 11) Let g : M → M be a partially hyperbolic diffeomorphism.”
• Entry and return times distribution (2013, methodology): “Another similar approach was used by Dolgopyat [42] where he derived a Poisson law for the limiting return times for a class of non-uniformly hyperbolic systems using characteristic functions.”
• AN INTRODUCTION TO QUANTITATIVE POINCARÉ RECURRENCE IN DYNAMICAL SYSTEMS (2009, unknown): “Few works considering return time to balls or natural sets [16, 17, 35, 20, 19] are emerging.”