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Details of Grant 

EPSRC Reference: GR/A01534/01
Title: AF: SPATIOTEMPORAL SYMMETRY IN HAMILTONIAN DYNAMICAL SYSTEMS
Principal Investigator: Lamb, Professor JS
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: Imperial College London
Scheme: Advanced Fellowship (Pre-FEC)
Starts: 31 March 2001 Ends: 30 March 2006 Value (£): 230,393
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
In order to understand the cosequences of symmetry in mechanical systems, we will study Hamiltonian dynamical systems with spatiotemporal symmetry. There exists a strong tradition in studying the consequences of continuous symmetries in Hamiltonian systems, but the proposed research will be complimentary to the geometric approach developed in that context. We will focus in particular on discrete symmetries, including time-reversal symmetries. This is important, because in most applications of interest discrete symmetries arise. The research will build on the success of the corresponding theory developed for dissipative systems with symmetries, which has contributed significantly to the understanding of complex phenomena such as pattern formation and spontaneous symmetry breaking in fluids and coupled cell systems. The research in this proposal will explain qualitative changes in dynamics when external parameters are varied (bifurcation theory) and shed light on how symmetry influences the occurrence of complicated dynamical behaviour (chaos). Among the many possible applications, the theory will be used to study the dynamics of molecules (with relavance to spectroscopy) and simple mechanical systems (with complicated dynamics) such as coupled pendula.
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Organisation Website: http://www.imperial.ac.uk