A topological characterization of certain postsingularly finite entire functions: transcendental dynamics and Thurston theory

Sergey SHEMYAKOV
I2M, Aix-Marseille Université
/user/sergey.shemyakov/

Date(s) : 10/01/2022   iCal
14 h 00 min - 16 h 00 min

Soutenance de thèse / Phd defense
(presentation in english)

Title: A topological characterization of certain postsingularly finite entire functions: transcendental dynamics and Thurston theory.
 
PhD adviser: Dierk Schleicher
Jury: upcoming
Abstract:
Holomorphic dynamics is an area of mathematics that studies the behavior of iterates of holomorphic and meromorphic functions. It has important connections with numerical analysis, general dynamical systems, and in particular topology and geometry, among many other directions. This thesis contributes to Thurston theory, an important field that connects the geometry of 3-manifolds, the structure of surface automorphisms, as well as holomorphic dynamics.
The main functions of interest in this thesis are “multi-error functions”; these generalize the exponential function with a single asymptotic tract, and the error-functions with two such tracts. These functions are given by the formula $g(z) = int_0^z e^{p(t)}dt$. We prove that a topological model of such a function is realized by a unique holomorphic map unless it admits a Levy cycle, which is one of the simplest topological multicurve obstructions.
Links :
theses.fr
Join Zoom Meeting
https://univ-amu-fr.zoom.us/j/95102500219?pwd=SGZ6OVlrOTNQb1FqM1hUSkhabDFMUT09

Meeting ID: 951 0250 0219
Passcode: see mail
Titre : Une caractérisation topologique de certaines fonctions entières post-singulièrement finies: dynamique transcendantale et théorie de Thurston.

Emplacement
FRUMAM, St Charles (2ème étage)

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