Danijela Damjanovic (KTH) : Rigidity for large group actions containing an Anosov element

An Anosov element of a smooth group action is a diffeomorphism contained in an action of a Lie group G which is uniformly hyperbolic with respect to the G-orbits. Generally, diffeomorphisms with some hyperbolic behaviour are representatives of chaotic dynamics and as such are typically not expected to have many symmetries. On the other hand, in the world of algebraic systems, which typically have many symmetries, Anosov elements are typical. This points to the question: can we use purely algebraic information on the structure of group of symmetries of a chaotic system (or information that the system embeds in certain Lie group) to classify the system as algebraic?  Rigidity theory in dynamical systems is an effort to provide smooth classification of those partially hyperbolic or Anosov systems that embed in large groups of diffeomorphisms and have many symmetries. 

I will give a brief introduction of main directions and questions in rigidity theory, and then present a rigidity result for higher-rank semisimple Lie group actions containing an Anosov element (joint work with Ralf Spatzier, Kurt Vinhage and Disheng Xu)