Dynamics of isometries of the hyperbolic plane

Ian Short, The Open University. Part of the analysis and applications seminar series.

The well-known Denjoy-Wolff theorem describes the behaviour of iterates of holomorphic self-maps of the unit disc. Our objective is to develop results of a similar type for nonautonomous dynamical systems, in which sequences of maps are generated by composing holomorphic maps from some given family. We make good progress for maps that are hyperbolic isometries, obtaining attractive connections between geometry and dynamics.

Ian Short, The Open University