Séminaire de Géométrie, Groupes et Dynamiques

Alexandra Skripchenko (HSE Moscow) : Systems of isometries in dynamics and topology

Systems of partial isometries of the interval represent a simple combinatorial object which appears in topology in connection with measured foliations on a surface (orientable or non-orientable), in dynamics as a nice model to study billiards in rational polygons and in geometric group theory as a way to describe actions of free groups on R-trees. We will discuss several classes of systems of isometries (interval exchange transformations, interval exchange transformations with flips,interval translation mappings, band complexes) and compare their basic dynamical properties: minimality, ergodicity, invariant measures etc. The talk is mainly based on the joint works with Artur Avila and Pascal Hubert and with Serge Troubetzkoy.
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