| EPSRC Reference: |
GR/R93025/01 |
| Title: |
Reversible Equivariant Hopf Bifurcation |
| Principal Investigator: |
Lamb, Professor JS |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
08 June 2002 |
Ends: |
07 June 2003 |
Value (£): |
6,047
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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We aim to carry out the study of reversible equivariant Hopf bifurcation. This development follows recent results on the classification of reversible equivariant linear systems (Lamb & Roberts (1999)), linear normal form theory for linear reversible equivariant systems (Hoveijn, Lamb & Roberts (2001)) and their Hamiltonian counterparts (Hoveijn, Lamb & Roberts (2001-2002)), and reversible equivariant steady-state bifurcation (Buono, Lamb & Roberts (2001-2002)). The classification presented in these studies (especially Lamb & Roberts (1999)) enables the systematic study of reversible equivariant Hopf bifurcation. Importantly, it turns out that previous studies of reversible equivariant Hopf bifurcation (and Liapunov centre Theorem) have been incomplete, in the sense that they turn out to have described only certain special cases and partial results. It is our aim to treat the Liapunov Centre Theorem (codimension zero) and Hopf Bifurcation (codimension one) in full extend, so as to match the theory in the equivariant case. A difference with the equivariant Hopf Theorem is that in the reversible equivariant context, there are more inequivalent types of generic Hopf bifurcation. Part of this difference stems from the fact that are different types of resonances that need to be considere, but even within the 1:1 resonance various different types arise. Importantly, we aim to extend our results to the Hamiltonian category, since there are many applications of interest (eg in Mechanics) in the context of which reversible equivariant Hamiltonian systems arise. It is our ultimate aim to highlight our results in this context.
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.imperial.ac.uk |