Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Gutachter "Bartholdi, Laurent Prof. Dr."
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Approximation of Baker domains and convergence of Julia sets.
(2013-05-14)The goal of this thesis is to prove the Hausdorff convergence of Julia sets as we approximate a family of transcendental entire functions featuring a unique Baker domain. At first, we give a dynamical description of the ... -
Chaos and Chaos Control in Network Dynamical Systems
(2013-01-16)Even fully deterministic dynamics may be chaotic, i.e., essentially unpredictable as time evolves. The first part of this thesis concerns the emergence of chaos in dynamical systems with symmetry, in particular certain ... -
Coarse Cohomology with twisted Coefficients
(2019-04-18)This thesis studies sheaf cohomology on coarse spaces. -
Computation with finitely L-presented groups
(2012-06-20)We develop algorithms for certain infinitely presented groups, the so-called finitely L-presented groups. For this purpose, we generalize the well-known algorithms for finitely presented groups to finite L-presentations. ... -
Equations in Self-Similar Groups
(2018-02-16)We introduce a method on how to decide solvebility of quadratic equations in self-similar groups and use this method to show that certain equations always have a solution. In particular the group of tree automorphisms and ... -
Growth in finite groups and the Graph Isomorphism Problem
(2020-08-19)The present thesis embraces two major areas of mathematics, namely group theory (especially growth in finite groups) and graph theory (especially the graph isomorphism problem). Several results are presented coming from ... -
Lie Algebras and the Dimension Problem
(2021-11-03)The dimension subgroup problem and the Ore conjecture are two group theoretical problems. In this thesis, translations of these problems to Lie algebras are analyzed and partially solved. -
On an analogue of L2-Betti numbers for finite field coefficients and a question of Atiyah
(2016-07-12)We construct a dimension function for modules over the group ring of an amenable group. This may replace the von Neumann dimension in the definition of L2-Betti numbers and thus allows an analogue definition for finite ... -
Rough Isometries of Order Lattices and Groups
(2009-12-07)We first introduce some basic concepts in metric geometry and order lattice theory. We then combine these concepts to study order lattices with metrics, in particular with view on the ...