Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems

Ai-Hua Fan (1) , Lingmin Liao (2) , Meng Wu (3)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 Department of Mathematical Sciences, P.O. Box 3000, 90014 University of Oulu, Finland.

In this paper, we study the multiple ergodic averages of a locally constant real-valued function in linear Cookie-Cutter dynamical systems. The multifractal spectrum of these multiple ergodic averages is completely determined.

Domaines: Systèmes dynamiques [math.DS]; Analyse classique [math.CA]

Ai-Hua Fan, Lingmin Liao, Meng Wu. Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems. 2012. ⟨hal-00723253v2⟩