Generic points in the Cartesian powers of the Morse dynamical system

Emmanuel Lesigne (1) , Anthony Quas (2) , Mate Wierdl (2)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 Department of Mathematics and Statistics

The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.

Mots clés: Morse sequence; weak disjointness

Domaines: Systèmes dynamiques [math.DS]

Emmanuel Lesigne, Anthony Quas, Mate Wierdl. Generic points in the Cartesian powers of the Morse dynamical system. Bulletin de la société mathématique de France, 2003, 131, pp.435-464. ⟨hal-00017103⟩