Second-order ergodic theorem for self-similar tiling systems

Konstantin Medynets; Boris Solomyak

doi:10.1017/etds.2013.27

Second-order ergodic theorem for self-similar tiling systems

Konstantin Medynets
, Boris Solomyak

United States Naval Academy
University of Washington

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider infinite measure-preserving non-primitive self-similar tiling systems in Euclidean space R^d. We establish the second-order ergodic theorem for such systems, with exponent equal to the Hausdorff dimension of a graph-directed self-similar set associated with the substitution rule.

Original language	English
Pages (from-to)	2018-2053
Number of pages	36
Journal	Ergodic Theory and Dynamical Systems
Volume	34
Issue number	6
DOIs	https://doi.org/10.1017/etds.2013.27
State	Published - 3 Apr 2013
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Cambridge University Press, 2013.

Funding

Funders	Funder number
National Stroke Foundation	DMS-0968879

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10.1017/etds.2013.27

Cite this

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AB - We consider infinite measure-preserving non-primitive self-similar tiling systems in Euclidean space Rd. We establish the second-order ergodic theorem for such systems, with exponent equal to the Hausdorff dimension of a graph-directed self-similar set associated with the substitution rule.

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Second-order ergodic theorem for self-similar tiling systems

Abstract

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