### Abstract

We consider a natural action τ of the group Z^{d} on the space X consisting of the functions x: Z^{d} → S (S-valued configurations on Z^{d}), where S is a finite set. For an arbitrary continuous function f: X → R^{m}, we study the multifractal spectrum of its time means corresponding to the dynamical system τ and a proper "averaging" sequence of finite subsets of the lattice Z^{d}, The main tool of the research is thermodynamic formalism.

Original language | English (US) |
---|---|

Pages (from-to) | 78-91 |

Number of pages | 14 |

Journal | Theory of Probability and its Applications |

Volume | 51 |

Issue number | 1 |

DOIs | |

State | Published - May 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Theory of Probability and its Applications*,

*51*(1), 78-91. https://doi.org/10.1137/S0040585X97982207

}

*Theory of Probability and its Applications*, vol. 51, no. 1, pp. 78-91. https://doi.org/10.1137/S0040585X97982207

**Multifractal analysis of time averages for continuous vector functions on configuration space.** / Gurevich, B. M.; Tempelman, Arkady.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Multifractal analysis of time averages for continuous vector functions on configuration space

AU - Gurevich, B. M.

AU - Tempelman, Arkady

PY - 2007/5/1

Y1 - 2007/5/1

N2 - We consider a natural action τ of the group Zd on the space X consisting of the functions x: Zd → S (S-valued configurations on Zd), where S is a finite set. For an arbitrary continuous function f: X → Rm, we study the multifractal spectrum of its time means corresponding to the dynamical system τ and a proper "averaging" sequence of finite subsets of the lattice Zd, The main tool of the research is thermodynamic formalism.

AB - We consider a natural action τ of the group Zd on the space X consisting of the functions x: Zd → S (S-valued configurations on Zd), where S is a finite set. For an arbitrary continuous function f: X → Rm, we study the multifractal spectrum of its time means corresponding to the dynamical system τ and a proper "averaging" sequence of finite subsets of the lattice Zd, The main tool of the research is thermodynamic formalism.

UR - http://www.scopus.com/inward/record.url?scp=34247490975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247490975&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97982207

DO - 10.1137/S0040585X97982207

M3 - Article

AN - SCOPUS:34247490975

VL - 51

SP - 78

EP - 91

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 1

ER -