Ahlfors Bers Colloquium
May
19-22, 2005
University of
Michigan
Ann Arbor, Michigan
Registration
Organizers
Dick
Canary
Juha
Heinonen
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Workshop
Abstract Detail
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Kevin Pilgrim Indiana University, Bloomington
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Coarse conformal dynamics
We define a notion of conformal expanding dynamical system for a map of a metric space to itself. The resulting theory is rich, and topological conjugacies between such systems are quasisymmetric. With a suitable definition of expanding, an expanding map $f$ from a compact metric space $X$ to itself admits, up to quasisymmetry, a unique compatible metric $d$ with respect to which the dynamics is conformal and expanding. From this it follows that the conformal dimension of $(X,d)$ is a topological invariant of the dynamical system $f: X \to X$. Examples and applications will be given. This is joint work in progress with P. Haissinsky. | ||
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