Dissertation (Metadaten)
Titel:Measurable dynamics of meromorphic maps
Autor:Jan-Martin Hemke
Fakultät:Mathematisch-Naturwissenschaftliche Fakultät
DDC Sachgebiet:510 Mathematik
Datum der mdl. Prüfung:02.06.2005
Referent(in):Prof. Dr. W. Bergweiler
Korreferent(en) Korreferentin:Prof: Dr. H. König
Beschreibung:We study how the orbits of the singularities of the inverse of a meromorphic function prescribe the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We concentrate on a family of entire transcendental functions with only finitely many singularities of the inverse, counting multiplicity, all of which either escape exponentially fast or are pre-periodic. For these functions we are able to decide, whether the function is recurrent or not. In the case that the Julia set is not the entire plane we also obtain estimates for the measure of the Julia set. MSC: 37F10}
Schlagworte:Iteration, meromorph, complex dynamics, rekurrent, Julia set, transcendental entire, dynamical systems, ergodic theory, analytic mappings, singularities of the inverse
Meromorphe Funktion ; Julia-Menge ; Iterationstheorie
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