Hausdorff dimension of the set of generic points for Gibbs measures

B. M. Gurevich; A. A. Tempelman

doi:10.1023/A:1020106306834

Hausdorff dimension of the set of generic points for Gibbs measures

B. M. Gurevich, A. A. Tempelman

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

4 Scopus citations

Abstract

For a Gibbs measure on the configuration space of a finite spin lattice system, we find (in terms of entropy) the Hausdorff dimension of the set of generic points. Using this result, we evaluate the Hausdorff dimension of level sets for Birkhoff ergodic averages of some continuous functions on the configuration space.

Original language	English (US)
Pages (from-to)	225-227
Number of pages	3
Journal	Functional Analysis and Its Applications
Volume	36
Issue number	3
DOIs	https://doi.org/10.1023/A:1020106306834
State	Published - 2002

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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title = "Hausdorff dimension of the set of generic points for Gibbs measures",

abstract = "For a Gibbs measure on the configuration space of a finite spin lattice system, we find (in terms of entropy) the Hausdorff dimension of the set of generic points. Using this result, we evaluate the Hausdorff dimension of level sets for Birkhoff ergodic averages of some continuous functions on the configuration space.",

author = "Gurevich, {B. M.} and Tempelman, {A. A.}",

note = "Funding Information: ∗The first author was partially supported by RFBR grant 02-01-00444.",

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language = "English (US)",

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journal = "Functional Analysis and Its Applications",

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AU - Gurevich, B. M.

AU - Tempelman, A. A.

N1 - Funding Information: ∗The first author was partially supported by RFBR grant 02-01-00444.

PY - 2002

Y1 - 2002

N2 - For a Gibbs measure on the configuration space of a finite spin lattice system, we find (in terms of entropy) the Hausdorff dimension of the set of generic points. Using this result, we evaluate the Hausdorff dimension of level sets for Birkhoff ergodic averages of some continuous functions on the configuration space.

AB - For a Gibbs measure on the configuration space of a finite spin lattice system, we find (in terms of entropy) the Hausdorff dimension of the set of generic points. Using this result, we evaluate the Hausdorff dimension of level sets for Birkhoff ergodic averages of some continuous functions on the configuration space.

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U2 - 10.1023/A:1020106306834

DO - 10.1023/A:1020106306834

M3 - Article

AN - SCOPUS:0036374122

SN - 0016-2663

VL - 36

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EP - 227

JO - Functional Analysis and Its Applications

JF - Functional Analysis and Its Applications

IS - 3

ER -

Hausdorff dimension of the set of generic points for Gibbs measures

Abstract

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