{"id":{"repo_id":"stellenbosch","oai_identifier":"oai:scholar.sun.ac.za:10019.1/135713"},"canonical_url":"https://search.dev.ndltd.org/etd/stellenbosch/oai:scholar.sun.ac.za:10019.1/135713","repository":{"repo_id":"stellenbosch","name":"Stellenbosch University","base_url":"https://scholar.sun.ac.za/server/oai/request"},"display":{"title":"Exceptional surfaces as topological obstructions in dynamical systems","abstract":"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?","abstract_html":"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?","abstract_has_math":false,"creators":["Davids, Keegan Michael"],"institution":"Stellenbosch : Stellenbosch University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Scholtz, F. G."],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-03","date_published":"2026-03","updated_at":"2026-07-24T04:40:09Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.sun.ac.za/handle/10019.1/135713","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Scholtz, F. G."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Stellenbosch University. Faculty of Science. Dept. of Physics."]},{"key":"dc:creator","label":"Author","values":["Davids, Keegan Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-04-08T11:52:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-04-08T11:52:11Z"]},{"key":"dc:date.issued","label":"Date","values":["2026-03"]},{"key":"dc:publisher","label":"Institution","values":["Stellenbosch : Stellenbosch University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://scholar.sun.ac.za/handle/10019.1/135713"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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"]},{"key":"dc:description.abstract","label":"Abstract","values":["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?"]},{"key":"dc:title","label":"Title","values":["Exceptional surfaces as topological obstructions in dynamical systems"]}]}],"canonical_facts":{"dc:contributor.advisor":["Scholtz, F. G."],"dc:contributor.other":["Stellenbosch University. Faculty of Science. Dept. of Physics."],"dc:creator":["Davids, Keegan Michael"],"dc:date.accessioned":["2026-04-08T11:52:11Z"],"dc:date.available":["2026-04-08T11:52:11Z"],"dc:date.issued":["2026-03"],"dc:description":["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"],"dc:description.abstract":["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? 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