Speaker: Chaitanya Tappu
We will define the n-dimensional hyperbolic space. An object of study in hyperbolic geometry is the group of isometries, i.e. distance preserving transformations of the hyperbolic space, and its action on the hyperbolic space. These correspond to Mobius transformations, and their action extends onto the boundary of the hyperbolic space. The action of discrete subgroups of this group has orbits that accumulate on the limit set, which lies on the boundary. We will show the construction of measures on the limit set which possess nice ergodicity properties with respect to this action.
Prerequisites: Familiarity with linear algebra and metric space topology will be assumed.
- Nicholls, P.J. (1989). The Ergodic Theory of Discrete Groups, vol. 143 of London Mathematical Society Lecture Note Series, Cambridge University Press