DnA Seminar, Daniel Cuzzocreo (Smith): 'Parameter space structures for rational maps'

Tuesday, April 21, 2015
12:00 PM - 1:00 PM (ET)
ESC 638
Event Type
Academic Calendar
David Constantine, x2171
Math CS DnA Seminar

Abstract: Fn,d,λ = zn + λ/zd give 1-parameter, n+d degree families of rational maps of the Riemann sphere, which arise as singular perturbations of the polynomial zn. Despite the high degree, symmetries cause these maps to have just a single free critical orbit and thus to form a natural 1-dimensional slice. Due to some similarities with polynomial maps, these families give some of the best-understood examples of non-polynomial rational dynamics in arbitrarily high degree. In this talk we give a survey of some recent results about these maps, with a focus on characterizing some of the fractal structure in the parameter space.

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