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Laminations and external angles for similarity pairs

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NPCW04 - Approximation, deformation, quasification

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. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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