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Zero Entropy System (1804)
Système d’entropie nulle
Dates: 27 November – 1 December 2017 at CIRM (Marseille Luminy, France)

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. 

  • Dou Dou (Nanjing University)

Entropy dimension for zero entropy systems (pdf)

Rigidity for square tiled interval exchange transformations

Sturmian numeration systems and decompositions to palindromes

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

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

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)

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