Laminations and external angles for similarity pairs
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About this item
| Description: |
Calegari, D (University of Chicago)
Friday 12th May 2017 - 11:00 to 12:00 |
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| Created: | 2017-05-22 10:12 |
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| Collection: | Non-Positive Curvature Group Actions and Cohomology |
| Publisher: | Isaac Newton Institute |
| Copyright: | Calegari, D |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | The Barnsley-Harrington Mandelbrot set for similarity pairs has many interesting affinities with the “usual” Mandelbrot set. In particular, there is a “coding” of boundary points by data analogous to the “external angle” for points on the boundary of the usual Mandelbrot set. Instead of a single real number - an external angle - there is another parameter, a “scale factor”, which can be between 1 and 2, and is 2 when the similarity pair is quasiconformally conjugate (as a conformal dynamical system on its limit set) to (the inverse of) a degree 2 rational map on its Julia set. As with the ordinary external angle, there is associated to the pair (angle, scale factor) a lamination of the circle which parameterizes cut points for the limit set. This is joint work with Alden Walker.
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