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Appears in collection : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

I will introduce the Speiser and Eremenko-Lyubich classes of transcendental entire functions and give a brief review of quasiconformal maps and the measurable Riemann mapping theorem. I will then discuss tracts and models for the Eremenko-Lyubich class and state the theorem that all topological tracts can occur in this class. A more limited result for the Speiser class will also be given. I will then discuss some applications of these ideas, focusing on recent work with Kirill Lazebnik (prescribing postsingular orbits of meromorphic functions) and Lasse Rempe (equilateral triangulations of Riemann surfaces).

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  • DOI 10.24350/CIRM.V.19810603
  • Cite this video Bishop, Christopher (20/09/2021). Transcendental functions with small singular sets. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19810603
  • URL https://dx.doi.org/10.24350/CIRM.V.19810603

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