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

## January 24, 2019 @ 4:00 pm - 5:00 pm

**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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