Mating quadratic maps with the modular group

Abstract: Holomorphic correspondences are multi-valued maps defined by polynomial relations $P(z,w)=0$. We consider a specific 1-(complex)parameter family of (2:2) correspondences (every point has 2 images and 2 preimages) which encodes both the dynamics of a quadratic rational map and the dynamics of the modular group. We show that the connectedness locus for this family is homeomorphic to the parabolic Mandelbrot set, itself homeomorphic to the Mandelbrot set. Joint work with S. Bullett.

complex variablesdynamical systems

Audience: researchers in the topic

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