| Citation | Known for fundamental results in qualitative dynamics ranging over a broad spectrum from deterministic to chaotic complex systems. Her work frequently begins with ingenious examples (or classes) and proceeds to a general explicatory theory. Such is the case with her striking example of a positive entropy minimal homeomorphism, her construction of point distal fibred maps with a rich diversity of fibre actions and her proof that the exponential map of the Riemann sphere is non?recurrent. Current work is a substantial contribution to the combinatorial and topological classification problem involving Teichmuller theory which appears in two monumental papers and which is the foundation of a forthcoming 200 page article. The work provides a thorough analysis of the variation of dynamics within the non-linear parameter family of degree 2 rational maps. She was the first to make a connection between the divergence type of non-compact geodesic flows, equilibrium states, and the Patterson?Sullivan boundary measure. Perhaps her most celebrated result is her proof of the existence of a positive measure set (in parameter space) of rational maps (of any degree) preserving an absolutely continuous measure; work which subsumes a substantial part, by adaptation, of Yakobson's renowned and analogous theorem for quadratic unimodal interval maps. |