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
14h00 - 16h00
(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.
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
– theses.fr
Emplacement
Saint-Charles - FRUMAM (2ème étage)
Catégories
