Multifractal analysis of some multiple ergodic averages

Summary, in English

In this paper we study the multiple ergodic averages, on the symbolic space σ_m = (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.

• Författare: Ai Hua Fan; Jörg Schmeling; Meng Wu
• Avdelning/ar: Matematik LTH; Dynamical systems
• Publiceringsår: 2016-06-04
• Språk: Engelska
• Sidor: 271-333
• Publikation/Tidskrift/Serie: Advances in Mathematics
• Volym: 295
• Länkar: http://dx.doi.org/10.1016/j.aim.2016.03.012
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematical Analysis
• Nyckelord: Hausdorff dimension; Multifractal; Multiple ergodic average
• Status: Published
• Forskningsgrupp: Dynamical systems
• ISBN/ISSN/Övrigt: ISSN: 0001-8708