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Exceptional surfaces as topological obstructions in dynamical systems
Thesis (MSc)--Stellenbosch University, 2026.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2026
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| _version_ | 1867613883442659328 |
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| access_status_str | Open Access |
| author | Davids, Keegan Michael |
| author2 | Scholtz, F. G. |
| author_browse | Davids, Keegan Michael Scholtz, F. G. |
| author_facet | Scholtz, F. G. Davids, Keegan Michael |
| author_sort | Davids, Keegan Michael |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2026. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/135713 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:13.574Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/135713 Exceptional surfaces as topological obstructions in dynamical systems Davids, Keegan Michael Scholtz, F. G. Stellenbosch University. Faculty of Science. Dept. of Physics. Thesis (MSc)--Stellenbosch University, 2026. Davids, K. M. 2026. Exceptional surfaces as topological obstructions in dynamical systems. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/545e5870-ef97-48c2-a0a1-1e4fe2c834da 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? Masters 2026-04-08T11:52:11Z 2026-04-08T11:52:11Z 2026-03 Thesis https://scholar.sun.ac.za/handle/10019.1/135713 en Stellenbosch University 64 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Davids, Keegan Michael Exceptional surfaces as topological obstructions in dynamical systems |
| title | Exceptional surfaces as topological obstructions in dynamical systems |
| title_full | Exceptional surfaces as topological obstructions in dynamical systems |
| title_fullStr | Exceptional surfaces as topological obstructions in dynamical systems |
| title_full_unstemmed | Exceptional surfaces as topological obstructions in dynamical systems |
| title_short | Exceptional surfaces as topological obstructions in dynamical systems |
| title_sort | exceptional surfaces as topological obstructions in dynamical systems |
| url | https://scholar.sun.ac.za/handle/10019.1/135713 |
| work_keys_str_mv | AT davidskeeganmichael exceptionalsurfacesastopologicalobstructionsindynamicalsystems |