| EPSRC Reference: |
GR/S78100/01 |
| Title: |
Dynamics of reversible systems near elliptic points |
| Principal Investigator: |
Lamb, Professor JS |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
15 December 2003 |
Ends: |
14 June 2005 |
Value (£): |
6,155
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
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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Elliptic fixed points are characterized by their neutral stability properties (eigenvalues on the complex unit circle). It is well known that there are two important categories of dynamical systems in which elliptic points robustly arise: Hamiltonian dynamical systems, and reversible dynamical systems. In the context of Hamiltonian dynamical systems, lots is known about the nature of the dynamics, which is roughly characterized by the existence of KAMtori and heteroclinic networks of saddle points. In the reversible (non-Hamiltonian) category, despite the parallel development of KAM theory for reversible and Hamiltonian dynamical systems, much less is known about the dynamics near elliptic points. The proposed research focusses on answering some major open questions on this topic. In particular, we will address the question whether dissipative dynamics is endemic near reversible (non-Hamiltonian) elliptic points. Our conjecture is that this is the case, which has the important corollary that dynamics near elliptic points in reversible dynamical systems is not conservative , as has often been suggested in the literature.
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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.imperial.ac.uk |