Professor Valérie Berthe, CNRS, University Paris Diderot, IRIF – Ergodic Theory Workshop

Title: Beyond Pisot dynamics

Abstract:  Pisot conjecture states that  substitutive  Pisot dynamics  implies  pure  discrete spectrum. We discuss in this lecture current extensions  with non-algebraic parameters, obtained  in collaboration with W. Steiner and J. Thuswaldner.  The Pisot assumption is formulated  in terms of Lyapunov exponents. We illustrate these extensions with  expansions issued from  multidimensional continued fraction algorithms, which yields  in particular  explicit symbolic codings for a.e. toral translation  on the two-dimensional torus. We  also  discuss  applications  to  the generation of  non-stationary Markov partitions and  to higher-dimensional  generalizations of  the three-length theorem.

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