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On mixing and the local central limit theorem for hyperbolic flows

Published online by Cambridge University Press:  11 May 2018

DMITRY DOLGOPYAT  and
PÉTER NÁNDORI
DMITRY DOLGOPYAT
Affiliation:
University of Maryland, Department of Mathematics, 4176 Campus Drive College Park, MD 20742-4015, USA email dmitry@math.umd.edu, pnandori@math.umd.edu
PÉTER NÁNDORI
Affiliation:
University of Maryland, Department of Mathematics, 4176 Campus Drive College Park, MD 20742-4015, USA email dmitry@math.umd.edu, pnandori@math.umd.edu
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Abstract

We formulate abstract conditions under which a suspension flow satisfies the local central limit theorem. We check the validity of these conditions for several systems including reward renewal processes, Axiom A flows, as well as the systems admitting Young’s tower, such as Sinai’s billiard with finite horizon, suspensions over Pomeau–Manneville maps, and geometric Lorenz attractors.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 1 , January 2020 , pp. 142 - 174
Copyright
© Cambridge University Press, 2018 

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