Description
Sarah Koch (University of Michigan):
In his last paper, "Entropy in Dimension One," W. Thurston completely characterized which algebraic integers arise as exp(entropy(f)), where f is a postcritically finite real map of a closed interval. On page 1 of this paper, there is a spectacular image of a subset in C comprised of roots of polynomials which come from entropy values associated to the dynamics of quadratic polynomials. This set displays some amazing fractal structure which can be (somewhat) understood when viewed as a distinguished subset of parameter space for a particular family of iterated function systems (IFS). In this talk, we investigate other distinguished subsets in parameter space for this IFS and prove some surprising results about their topology. We compare/contrast the discussion of this parameter space to the study of the parameter space for quadratic polynomials pc:z → z2+c.
This is joint work with D. Calegari and A. Walker.
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