Multifractal analysis of some multiple ergodic averages
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 mea
