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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 

 

Limit theorems for partially hyperbolic systems


Author: Dmitry Dolgopyat
Journal: Trans. Amer. Math. Soc. 356 (2004), 1637-1689
MSC (2000): Primary 37D30; Secondary 60Fxx
Published electronically: September 22, 2003
MathSciNet review: 2034323
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Abstract: We consider a large class of partially hyperbolic systems containing, among others, affine maps, frame flows on negatively curved manifolds, and mostly contracting diffeomorphisms. If the rate of mixing is sufficiently high, the system satisfies many classical limit theorems of probability theory.


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Additional Information

Dmitry Dolgopyat
Affiliation: Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
Email: dmitry@math.umd.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03335-X
Keywords: Partial hyperbolicity, central limit theorem, Gibbs measure, absolute continuity
Received by editor(s): April 17, 2002
Received by editor(s) in revised form: March 19, 2003
Published electronically: September 22, 2003
Additional Notes: This work was partly supported by an Elisabeth Proctor Fellowship at Princeton, a Miller Fellowship at Berkeley, and a Sloan Fellowship at PennState
Article copyright: © Copyright 2003 by the author