| EPSRC Reference: |
GR/M05508/01 |
| Title: |
BIFURCATION OF REDUCED PHASE SPACES II |
| Principal Investigator: |
Roberts, Professor M |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
12 March 1998 |
Ends: |
11 January 1999 |
Value (£): |
7,400
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Symmetric Hamiltonian systems are used to model the dynamics of phenomena as diverse as atomic nuclei, molecules, self-gravitating fluid masses and planetary systems. Reduction techniques are applied to factor out the symmetries, yielding families of Hamiltonian systems defined on reduced phase spaces of lower dimensions and parametrized by conserved quantities (momentum).The research proposed here is the second phase of a project to describe the ways the topology and geometry of the reduced phase spaces can change as momentum varies. The first step will be to use local normal forms for Hamiltonian G-manifolds to obtain local descriptions of the topological changes. These will then be combined with a stratification theorem for momentum maps, proved in the first phase, to obtain descriptions of the global changes. The results obtained will generalise well known results for free actions on contingent bundles and results of Guillemin and Sternberg for torus actions.The stratification theorem will also be used to describe the variation of the symplectic structures on reduced phase spaces that occurs as momentum is varied, even when the topology remains constant. These results will generalise a theorem of Duistermaat and Heckman for torus actions.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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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 |
| Summary |
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| Date Materialised |
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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.warwick.ac.uk |