Multifractal analysis of some multiple ergodic averages
(2016) In Advances in Mathematics 295. p.271-333- Abstract
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... (More)
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.
(Less)
- author
- Fan, Ai Hua ; Schmeling, Jörg LU and Wu, Meng
- organization
- publishing date
- 2016-06-04
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Hausdorff dimension, Multifractal, Multiple ergodic average
- in
- Advances in Mathematics
- volume
- 295
- pages
- 63 pages
- publisher
- Elsevier
- external identifiers
-
- wos:000376472400007
- scopus:84962228302
- ISSN
- 0001-8708
- DOI
- 10.1016/j.aim.2016.03.012
- language
- English
- LU publication?
- yes
- id
- b8135123-1799-44ab-b2c5-44e0a702e245
- date added to LUP
- 2016-04-27 16:19:53
- date last changed
- 2024-02-18 16:25:59
@article{b8135123-1799-44ab-b2c5-44e0a702e245,
abstract = {{<p>In this paper we study the multiple ergodic averages, on the symbolic space σ<sub>m</sub> = (0,1,...,m-1}<sup>N</sup>* 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.</p>}},
author = {{Fan, Ai Hua and Schmeling, Jörg and Wu, Meng}},
issn = {{0001-8708}},
keywords = {{Hausdorff dimension; Multifractal; Multiple ergodic average}},
language = {{eng}},
month = {{06}},
pages = {{271--333}},
publisher = {{Elsevier}},
series = {{Advances in Mathematics}},
title = {{Multifractal analysis of some multiple ergodic averages}},
url = {{http://dx.doi.org/10.1016/j.aim.2016.03.012}},
doi = {{10.1016/j.aim.2016.03.012}},
volume = {{295}},
year = {{2016}},
}