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Variations on a central limit theorem in infinite ergodic theory

Published online by Cambridge University Press:  04 June 2014

DAMIEN THOMINE
DAMIEN THOMINE*
Affiliation:
Université de Rennes 1, Rennes, France email [email protected]
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Abstract

In a previous paper the author proved a distributional convergence for the Birkhoff sums of functions of null average defined over a dynamical system with an infinite, invariant, ergodic measure, akin to a central limit theorem. Here we extend this result to larger classes of observables, with milder smoothness conditions, and to larger classes of dynamical systems, which may no longer be mixing. A special emphasis is given to continuous time systems: semi-flows, flows, and $\mathbb{Z}^{d}$-extensions of flows. The latter generalization is applied to the geodesic flow on $\mathbb{Z}^{d}$-periodic manifolds of negative sectional curvature.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 5 , August 2015 , pp. 1610 - 1657
Copyright
© Cambridge University Press, 2014 

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