| EPSRC Reference: |
GR/S50663/01 |
| Title: |
Rigidity of orbit spectra for hyperbolic systems |
| Principal Investigator: |
Pollicott, Professor M |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
Victoria University of Manchester, The |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
15 July 2003 |
Ends: |
14 October 2003 |
Value (£): |
2,993
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
One of the most elegant and influencial areas in mathematics is that of geometry of Riemann surfaces. It is a classical problem to recover a Riemann metric from a knowledge of the lengths of closed orbits (or equivalently the spectrum of the laplacian). The aim of this proposal is to study Holder functions for hyperbolic diffeomorphisms and flows. By analogy with the Riemann surface problem, we can consider the extent to which the Holder function can be recovered from the weightings it gives to closed orbits. In the special case of zero dimensional diffeomorphisms this corresponds to the situation for subshifts of finite type, which was studied by Weiss and Pollicott in a recent paper. Using these insights, we hope to study the rigidity problem in the general case of diffeomorphisms (and flows). We also want to study the extend to which dynamical invariants contribute back to the geometric setting to give new invariants.
|
|
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: |
|