Exceptional surfaces as topological obstructions in dynamical systems

We extend topological methods, originally used in the study of topological insulators, to the general nonlinear differential system. In particular, we develop a formulation of the Berry phase for classical dynamical systems and demonstrate its usage on a toy-model. Thereafter we discuss classical eigensystem degeneracy and analyse its topological properties as an exceptional surface (ES). Upon identifying the limitations of this formalism in higher dimensional systems, we develop a formulation of an "edge insertion" describing a singular adjustment made to any path that crosses a degeneracy in the correlating eigensystem. This repertoire of methods is subsequently applied to the Lorenz system and a reduced version thereof. This work raises a multitude of open questions including; which invariants are most effective at illuminating the topology of the system? How do degeneracies and ESs influence the underlying dynamics of the system?

Grantor dc:publisher

Stellenbosch : Stellenbosch University

Year dc:date.issued

2026

Author dc:creator

• Davids, Keegan Michael

Advisor dc:contributor.advisor

• Scholtz, F. G.

Language dc:language.iso

en

Repository record dc:identifier.uri

https://scholar.sun.ac.za/handle/10019.1/135713

OAI identifier oai:identifier

oai:scholar.sun.ac.za:10019.1/135713