Starts 30 Jul 2020 16:00
Ends 30 Jul 2020 17:00
Central European Time
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Abstract: Holomorphic correspondences are polynomial relations P(z,w)=0, which can be regarded as multi-valued self-maps of the Riemann sphere(implicit maps sending z to w). The iteration of such multi-valued map generates a dynamical system on the Riemann sphere (dynamical system which generalise rational maps and finitely generated Kleinian groups). We consider a specific 1-(complex)parameter family of (2:2) correspondences F_a (introduced by S. Bullett and C. Penrose in 1994), which we describe dynamically. In particular, we show that for every a in the connectedness locus M_{\Gamma}, this family is a mating between the modular group and rational maps in the family Per_1(1), and we develop for this family a complete dynamical theory which parallels the Douady-Hubbard theory of quadratic polynomials. This is joint work with S. Bullett.