Quadratic Rational Maps and Asymptotics of Transversality

par Jan Kiwi

vendredi 8 mars 2024, 10:30 → 11:30 Europe/Paris

207 (Bat 1R2)

In the complex two-dimensional parameter space of quadratic rational maps, it is of interest to study dynamically defined one-dimensional slices. An interesting collection of such slices are the curves formed  by maps having a periodic critical point, of a given period.  We obtain a formula for the Euler Characteristic of these curves. The formula is an application of the study of degenerate holomorphic families of quadratic rational maps with tools from non-Archimedean dynamics.