| EPSRC Reference: |
GR/M36335/02 |
| Title: |
THE DYNAMICS OF DISCONTINUOUS AREA-PRESERVING MAPS AND SIGNAL PROCESSING |
| Principal Investigator: |
Ashwin, Professor P |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematical Sciences |
| Organisation: |
University of Exeter |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 2000 |
Ends: |
31 March 2002 |
Value (£): |
64,682
|
| 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 |
|
We propose to look at the dynamics of discontinuous area-preserving elliptic maps, some of their applications to information processing and mechanical systems and generalisations of them.The simplest maps in this class are piecewise linear and have a Jacobian whose eigenvalues lie on the unit circle. On examining the set of all points that go arbitrarily close to the discontinuity, it is clear that this is highly ordered but badly understood. We want to understand the topology, measure and dynamics of such trajectories, and of such trajectories in related maps. They can display complicated dynamics while keeping zero Lyapunov exponents.Such maps arise naturally in signal processing, in particular in digital filters with overflow and in Sigma-Delta modulators where the discontinuity is associated with either switching in an electronic circuit or overflow in arithmetic. They arise in impacting systems such as polygonal billiards and dual billiards.
|
|
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.ex.ac.uk |