### Topological mixing of the Weyl Chamber flow

Ergodic Theory and Dynamical Systems Seminar

29th October 2020, 2:00 pm – 3:00 pm

Zoom,

Let $G$ be a semisimple Lie group of non-compact type (for instance $\mathrm{SL}(n,\mathbb{R})$) and $\Gamma$ be a Zariski dense discrete subgroup.

Choose a Cartan subspace $A$ and a maximal compact subgroup $K$, denote by $M$ the centralizer subgroup of $A$ in $K$.

I am interested in the dynamical properties of right action of one parameter subgroups $\phi^t$ of $A$ on $\Gamma \backslash G/M$.

For $\mathrm{PSL}(2,\mathbb{R})$, this action identifies with the geodesic flow on the unit tangent bundle of $\Gamma \backslash \mathbb{H}^2$ which is mixing on its non-wandering set.

My talk addresses the case when $A$ is of higher dimension and $\Gamma$ is not a lattice.

I will present a joint work with O. Glorieux: a necessary and sufficient condition for topological mixing of regular Weyl chamber flows.

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