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Multifractal analysis of some multiple ergodic averages

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Author

Summary, in English

In this paper we study the multiple ergodic averages, on the symbolic space σm = (0,1,...,m-1}N* where m≥ 2, ℓ ≥ 2, q≥ 2 are integers. We give a complete solution to the problem of multifractal analysis of the limit of the above multiple ergodic averages. Actually we develop a non-invariant and non-linear version of thermodynamic formalism that is of its own interest. We study a large class of measures (called telescopic product measures). The special case of telescopic product measures defined by the fixed points of some non-linear transfer operators plays a crucial role in studying the level sets of the limit, which are not shift-invariant. These measures share many properties with Gibbs measures in the classical thermodynamic formalism. Our work also concerns variational principle, pressure function and Legendre transform in this new setting.

Department/s

Publishing year

2016-06-04

Language

English

Pages

271-333

Publication/Series

Advances in Mathematics

Volume

295

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematical Analysis

Keywords

  • Hausdorff dimension
  • Multifractal
  • Multiple ergodic average

Status

Published

Research group

  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 0001-8708