| EPSRC Reference: |
GR/R73232/01 |
| Title: |
Conformal Measures and Holomorphic Correspondences |
| Principal Investigator: |
Bullett, Professor S |
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| Department: |
Sch of Mathematical Sciences |
| Organisation: |
Queen Mary University of London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 2002 |
Ends: |
31 March 2005 |
Value (£): |
145,777
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Holomorphic correspondences are a class of one dimensional complex dynamical systems embracing in a single mathematical framework both the dynamics of rational maps and Kleinian groups. There are striking parallels between the latter two theories - the celebrated 'Sufivan dictionary'.For large classes of correspondences, such as matings of Fuchsian groups with polynomial maps, there are well-defined limit sets on which the dynamical behaviour is a combination of that of a rational map and that of a Kleinian group. On one side of the limit sets there is a neighborhood in which the dynamics is conformally conjugate to that of the group and on the other side conjugate to that of the rational map. The limit sets are well-understood combinatorially (topologically) but nothing is yet known about their mebidmeasure theoretic properties. The main thrust of this proposal is to undertake such a study. By exploiting the sophisticated methodsdeveloped for rational maps and Meinian groups, the aim is to obtain measure and dimension results for the limit sets of these mixed systems and thereby develop more of a common framework embracing the measure theoretic entries on the two sides of Sullivan's dictionary. In short, this would involve constructing 'conformar measures on the Omit sets of correspondences analogous to those of Patterson and Sulfvan in the separate theories.
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Potential use in non-academic contexts |
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| Description |
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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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