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SUMMARY:Graduate Student Colloquium: Kelsey Brouwer
DESCRIPTION:Combinatorial Models for Some Generalized McMullen Maps in the Case of Two Bounded Critical Orbits\nKelsey Brouwer\nPhD Student\nUniversity of Wisconsin – Milwaukee \nThe family of generalized McMullen maps R(z)= z^n + b + a/z^n has two independent critical orbits. We consider the case in which one critical value lies in the immediate basin of an attracting cycle and the other critical value eventually lands in that immediate basin. Computer-generated images of the dynamical plane suggest the presence of both baby quadratic Julia sets and some sets which appear to be modifications of those. We present combinatorial models of the dynamics which help to explain this phenomena.
URL:https://uwm.edu/math/event/graduate-student-colloquium-kelsey-brouwer/
LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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SUMMARY:Colloquium: Dr. Daniel Stoertz
DESCRIPTION:Baby Mandelbrot Sets for Maximally Generalized McMullen Maps\nDr. Daniel Stoertz\nVisiting Assistant Professor of Mathematics\nSt. Olaf College \nIn Complex Dynamics\, we study the iteration of holomorphic or meromorphic functions on the complex plane or the Riemann sphere. Of particular interest is the behavior of the critical orbits of function families with one or more parameters. The simplest of such families\, z^2 +c\, is well-known to define the famous Mandelbrot set fractal as the set of c-values for which the unique critical orbit is bounded. In this talk we will examine the function family R(z) = z^n +b +a/(z^d)\, and we will explore old and new results establishing the location of baby Mandelbrot sets in parameter space for increasingly general versions of this family. In the most general case\, which we call maximally generalized McMullen maps\, this family has multiple independent critical orbits\, and the dynamics in this case are not yet well understood.
URL:https://uwm.edu/math/event/colloquium-dr-daniel-stoertz/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
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