The Modular Mandelbrot Set
Adventurous Berkeley Complex Dynamics May 02, 2022 - May 06, 2022
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
The Modular Mandelbrot Set
The Modular Mandelbrot set is the connectedness locus of a family of (2:2) correspondences (introduced by Bullett and Penrose in 1994). We show that these correspondences are matings between the modular group and the family of quadratic rational maps P_A(z)=z+1/z+A, and that there exists a dynamical homeomorphism between the modular Mandelbrot set and the parabolic Mandelbrot set (this last being the connectedness locus of the family P_A(z), and is itself homeomorphic to the classical Mandelbrot set by a result of Petersen and Roesch). The talk is based on joint work with Shaun Bullett.
The Modular Mandelbrot Set
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.