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

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

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

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1017/etds.2013.27

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title = "Second-order ergodic theorem for self-similar tiling systems",

abstract = "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.",

author = "Konstantin Medynets and Boris Solomyak",

note = "Publisher Copyright: {\textcopyright} Cambridge University Press, 2013.",

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doi = "10.1017/etds.2013.27",

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AU - Solomyak, Boris

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N2 - 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.

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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DO - 10.1017/etds.2013.27

M3 - مقالة

SN - 0143-3857

VL - 34

SP - 2018

EP - 2053

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 6

ER -

Second-order ergodic theorem for self-similar tiling systems

Abstract

All Science Journal Classification (ASJC) codes

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