In this small workshop, we discuss zero entropy systems, focusing on renormalization scheme, having in mind applications to number theoretical algorithms. 

Such systems are of zero entropy in additive action, but of positive entropy in renormalization structure, and form a nice pair of dynamical systems whose fundamental example is given by irrational rotations and classical continued fraction. 

• Shigeki Akiyama (University of Tsukuba & Aix–Marseille Université)
• Pierre Arnoux (Aix–Marseille Université)
• Nicolas Bédaride (Aix-Marseille Université)
• Fabien Durand (Université de Picardie Jules Verne)
• Sébastien Ferenczi (CNRS, Aix-Marseille Université)
• Bryna Kra (Northwestern University)
• Richard Schwartz (Brown University)​
• Boris Solomyak (University of Bar-Ilan)

• Dou Dou (Nanjing University)

Entropy dimension for zero entropy systems (pdf)

• Sébastien Ferenczi (CNRS, Aix-Marseille Université)

Rigidity for square tiled interval exchange transformations

• Anna Frid (Aix-Marseille Université)

Sturmian numeration systems and decompositions to palindromes

• Arek Goetz (San Francisco State University)

Lecture 1. Piecewise Isometries – The beautiful. Charm, intrigue, and the unknown
Lecture 2.  Piecewise Isometric research – Quo vadis?

• Pascal Hubert (Aix-Marseille Université)

Novikov’s problem on foliations and Arnoux-Rauzy interval exchange transformations

• John Lowenstein (New York University)

Lecture 1. Pseudochaotic Kicked-Oscillator Maps and Parametric Piecewise Isometries (pdf)
Lecture 2.  Global Scaling in a One-Parameter Family of Parametric Kicked-Oscillator Maps (pdf)

• Paul Mercat (Aix-Marseille Université)

Rauzy fractals, one dimensional Meyer sets, β-numeration and automata