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Classification of two-parameter bifurcations
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Peters, Martin Heinrich (1991) Classification of two-parameter bifurcations. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3226436~S15
Abstract
This thesis contains the classification of two-parameter bifurcations up to codimension three, using a two-parameter version of parametrised contact equivalence.
Part one contains the classification up to codimension one. The result consists of the following components:
1. A list of normal forms for the germs having codimension less or equal to one.
2. Recognition conditions for each normal form in the list, i. e. conditions that characterise the equivalence class of the normal form. These conditions are equations and inequalities for the Taylor coefficients of the germs.
3. Universal unfoldings for each normal form.
The result is obtained by investigating the structure of the orbits, which are induced by the action of the group of equivalences on the space of all bifurcation problems. Techniques from algebra, algebraic geometry and singularity theory are applied.
In part two the classification is extended to codimension three. The second chapter of part two contains a generalisation of the singularity approach to equivariant bifurcation theory. The case of an action of a compact Lie group on state and parameter space is considered. The main example is the case of bifurcations with a certain D4-symmetry.
| Item Type: | Thesis (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Bifurcation theory, Germs (Mathematics) | ||||
| Official Date: | May 1991 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Stewart, Ian, 1945- | ||||
| Sponsors: | University of Warwick | ||||
| Format of File: | |||||
| Extent: | vi, 155 leaves : illustrations | ||||
| Language: | eng |
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