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| Hovedforfatter: | |
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| Format: | Preprint |
| Udgivet: |
1999
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| Fag: | |
| Online adgang: | https://arxiv.org/abs/math/9910176 |
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Indholdsfortegnelse:
- The classical pitchfork of singularity theory is a twice-degenerate bifurcation that typically occurs in dynamical system models exhibiting Z_2 symmetry. Non-classical pitchfork singularities also occur in many non-symmetric systems, where the total bifurcation environment is usually more complex. In this paper three-dimensional manifolds of critical points, or limit-point shells, are introduced by examining several bifurcation problems that contain a pitchfork as an organizing centre. Comparison of these surfaces shows that notionally equivalent problems can have significant positional differences in their bifurcation behaviour. As a consequence, the parameter range of jump, hysteresis, or phase transition phenomena in dynamical models (and the physical systems they purport to represent) is determined by other singularities that shape the limit-point shell.