| EPSRC Reference: |
GR/R40807/01 |
| Title: |
Dynamics and Arithmetic |
| Principal Investigator: |
Pollicott, Professor M |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Manchester, The |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 January 2002 |
Ends: |
31 December 2004 |
Value (£): |
114,639
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The proposed research deals with canonical codings for simple arithmetic systems, such as hyperbolic toral automorphisms. The objective is to find a more natural way in which to model the underlying dynamical system (both topologically and measure theoretically) than the usual somewhat ad hoc method of Markov Partitions.There is considerable evidence in the preliminary results that such a natural correspondence exists, but the major problem is to put this into a general framework. The more familiar approach of Markov Partitions has proved very successful, in as much as it is frequently possible to establish results for the dynamical system via the associated correspondence with a symbolic model. The aim of this proposal is to establish, for arithmetic systems which have a natural additional group structure on the manifold, a better correspondence with a symbolic model which preserves even more structure. For example, at the level of measures, we would expect that this would give a clear insight into generalizations of the famous Erdos result on random distributions.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.man.ac.uk |