Seminar

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If a quadratic birational map f fixing a cubic with one singularity is birationally equivalent to an automorphism on a rational surface, its coordinate functions are in \mathbb{Z}(\alpha)[x,y,z] where \alpha is either the dynamical degree of f or one of its Galois conjugates. Thus, there are rational surface automorphisms with real coefficients for each given dynamical degree. i.e., There are two closed elated dynamical systems: Real and Complex dynamics. As the first step toward understanding their relation, we estimate the topological entropy using the growth rate in the Homology group (Joint work with J. Diller)  and the growth rate in the Fundamental group (Joint work with E. Klassen). In this talk, we will discuss how to get those estimations and what we found from these estimations.

Rational Surface Automorphisms: Real and Complex Dynamics 3.25 MB application/pdf

COMD Research Seminar Series: "Rational Surface Automorphisms: Real And Complex Dynamics"