Sören von der Gracht

Universität Paderborn | UPB · Department of Mathematics

We prove that steady state bifurcations in finite-dimensional dynamical systems that are symmetric with respect to a monoid representation generically occur along an absolutely indecomposable subrepresentation. This is stated as a conjecture in B. Rink and J. Sanders, "Coupled cell networks and their hidden symmetries", SIAM J. Math. Anal., 46 (201...

Dynamical systems often admit geometric properties that must be taken into account when studying their behaviour. We show that many such properties can be encoded by means of quiver representations. These properties include classical symmetry, hidden symmetry and feedforward structure, as well as subnetwork and quotient relations in network dynamic...

We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback) can be defined by a partial order on the cells. We use this property to study generic one-parameter steady state bifurcations for such networks. Branching solutions and their asymptotics are described in terms of Taylor coefficients of...

We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback loops) can be defined by a partial order on the cells. We use this property to study generic one-parameter steady state bifurcations for such networks. Branching solutions and their asymptotics are described in terms of Taylor coefficien...

The authors of Berg et al. [J. Algebra 348 (2011) 446–461] provide an algorithm for finding a complete system of primitive orthogonal idempotents for CM, where M is any finite R-trivial monoid. Their method relies on a technical result stating that R-trivial monoids are equivalent to so-called weakly ordered monoids. We provide an alternative algor...

Dynamical systems often admit geometric properties that must be taken into account when studying their behaviour. We show that many such properties can be encoded by means of quiver representations. These properties include classical symmetry, hidden symmetry and feedforward structure, as well as subnetwork and quotient relations in network dynamic...

The authors of [Primitive orthogonal idempotents for R-trivial monoids, Journal of Algebra] provide an algorithm for finding a complete system of primitive orthogonal idempotents for CM, where M is any finite R-trivial monoid. Their method relies on a technical result stating that R-trivial monoids are equivalent to so-called weakly ordered monoids...

In this paper we continue the study of group representations which are counterexamples to the Ize conjecture. As in the previous papers by Lauterbach [14] and Lauterbach & Matthews [15] we find new infinite series of finite groups leading to such counterexamples. These new series are quite different from the previous ones, for example the group ord...