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Laminations and external angles for similarity pairs

Presented by: 
Danny Calegari University of Chicago
Date: 
Friday 12th May 2017 - 11:00 to 12:00
Venue: 
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons