| EPSRC Reference: |
GR/L60029/01 |
| Title: |
SPATIO-TEMPORAL SYMMETRY IN DYNAMICAL SYSTEMS |
| Principal Investigator: |
Roberts, Professor M |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 December 1997 |
Ends: |
30 November 2000 |
Value (£): |
118,576
|
| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
|
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The aim of this project is to develop a theory for dynamical systems with spatio-temporal symmetries which simultaneously generalises the existing theories for equivariant and time-reversible systems and the emerging theory of k-symmetric maps. Systems with these general spatio-temporal symmetry groups arise naturally (often as return mappings) in a wide variety of applications including fluid and plasma dynamics and mechanics.Specific aims of the research include developing linear stability and local bifurcation theories using ideas and techniques from group theory, normal form theory and singularity theory. These theories will be developed for both general dynamical systems and Hamiltonian systems. The structure and possible symmetry groups of attractors of dynamical systems with general spatio-temporal symmetry groups will also be investigated and these results extended to the omega-limit sets with weaker stability properties that occur in Hamiltonian and time-reversible systems.A number of model applications will be considered including return maps for periodic fluid flows, cross-sections through stellerator plasma flows and the stability of relative equilibria and periodic orbits of symmetric mechanical systems.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.warwick.ac.uk |