ERGODIC THEOREMS FOR ACTIONS OF HYPERBOLIC GROUPS

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ERGODIC THEOREMS FOR ACTIONS OF HYPERBOLIC GROUPS

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by Mark Pollicott , Richard Sharp

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BibTeX

@MISC{Pollicott_ergodictheorems,
    author = {Mark Pollicott and Richard Sharp},
    title = {ERGODIC THEOREMS FOR ACTIONS OF HYPERBOLIC GROUPS},
    year = {}
}

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Abstract

Abstract. In this note we give a short proof of a pointwise ergodic theorem for measure preserving actions of word hyperbolic groups, also obtained recently by Bufetov, Khristoforov and Klimenko. Our approach also applies to infinite measure spaces and one application is to linear actions of discrete groups on the plane. The well-known Birkhoff ergodic theorem for ergodic transformations T: X → X on a probability space (X, B, µ) gives that the averages of an L 1 function along almost every orbit is equal to the integral of the function. If we view the transformation as a Z-action, then it is natural to ask about pointwise ergodic theorems

Keyphrases

ergodic theorem action hyperbolic group pointwise ergodic theorem probability space well-known birkhoff ergodic theorem short proof word hyperbolic group linear action discrete group ergodic transformation measure space

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