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Multifractal analys...
Multifractal analysis of some multiple ergodic averages
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- Fan, Ai Hua (författare)
- Central China Normal University (CCNU),University of Picardie Jules Verne
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- Schmeling, Jörg (författare)
- Lund University,Lunds universitet,Dynamiska system,Forskargrupper vid Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Dynamical systems,Lund University Research Groups,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Wu, Meng (författare)
- University of Picardie Jules Verne
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(creator_code:org_t)
- Elsevier BV, 2016
- 2016
- Engelska 63 s.
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708. ; 295, s. 271-333
- Relaterad länk:
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http://dx.doi.org/10...
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https://doi.org/10.1...
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https://lup.lub.lu.s...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Hausdorff dimension
- Multifractal
- Multiple ergodic average
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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