| EPSRC Reference: |
GR/K75453/01 |
| Title: |
PARAMETER SPECES OF RATIONAL MAPS |
| Principal Investigator: |
Rees, Professor SM |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematical Sciences |
| Organisation: |
University of Liverpool |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
18 October 1995 |
Ends: |
17 October 1998 |
Value (£): |
95,590
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The best understood parameter family of rational maps is that of quadratic polynomials. The general aim of this proposal is to increase our understanding of other parameter families of rational maps. The principal investigator has worked on a particular family (quadratic rational maps) for about 10 years. A potential RA (Ross Jones) is interested in the same general problem but has worked on it from a very different angle. It seems that the difficulties in considering parameter spaces other than quadratic polynomials split into two types. On the one hand, there are parameter spaces (such as the space of all degree d rational maps) in which variation of dynamics is non-monotone; it is impossible to find a set of combinatoral models which is naturally in one-to-one correspondence with the different conjugacy classes (including hyperbolic components) in the parameter family. This class of parameter spaces needs further study, even in the case of familities of one complex dimension. On the other hand, there are parameter spaces of higher degree polynomials, where the higher dimension of the family necessitates extensions of the theory for quadratic polynomials. These extensions seem possible and there should be a very complete theory for these families.
|
|
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.liv.ac.uk |