# Fingers in the parameter space of the complex standard family

The event is taking part on the Tuesday, Oct 17th 2017 at 15:30
Theme/s: Pure Maths
Location of Event: Alan Turing Room 306
This event is a: Public Seminar

Abstract: We study the parameter space of the complex standard family $$F_{\alpha,\beta}(z)=z+\alpha+\beta \sin z,$$ where the parameter $0<\beta\ll 1$ is considered to be fixed and the bifurcation is studied with respect to the parameter $\alpha\in\mathbb{C}$. In the real axis of that parameter plane one can observe the so-called Arnold tongues, and attached to them there are some finger-like structures which were observed for the first time by Fagella in her PhD thesis. Similar structures can also be observed in the parameter spaces of families of Blaschke products or Henon maps in higher dimension. We study the qualitative and quantitative aspects of these fingers via parabolic bifurcation.
This is a work in progress joint with Mitsuhiro Shishikura (Kyoto University