ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 58 Rees, Mary, University of Liverpool, U. K. . Using Teichmüller Geometry We write T for the Teichmüller space of a compact surface S_{0} with finite A_{0} ⊂ S_{0}. The Nielsen-Thurston isotopy-classification of a homeomorphism χ of (S_{0}, A_{0}), and a topological description of {ϕ ∘ χ ∘ ψ^{−1} : [ϕ] = [ψ]}, can be found [Bers] by analysing the set {[ϕ] ∈ T : d_{T} ([ϕ], [ϕ∘χ]) is minimised}. Now let f_{0} : (Ĉ, A_{0}) → (Ĉ, A_{0}) be an orientation-preserving branched covering with critical value set V_{0}. We shall indicate how the calculus of Teichmüller distance assists, analogously, in a topological description of the (usually topologically infinite) space {ϕ ∘ f_{0} ∘ ψ^{−1} : [ϕ] = [ψ]}.