Wiggly phenomena of the tricorn

開催日時
2014/10/10 金 14:00 - 17:00
場所
6号館609号室
講演者
稲生 啓行
講演者所属
京都大学大学院理学研究科
概要

The tricorn is the connectedness locus of the family of anti-holomorphic quadratic polynomials. Hubbard and Schleicher proved that many "umbilical cords" of hyperbolic components, which seem to connect them to the main hyperbolic component in numerical pictures, do not land. This result strongly suggests that "baby tricorn-like sets" are not homeomorphic to the tricorn itself, unlike in the case of the Mandelbrot set. We apply their method to other situation, such as umbilical cords inside "baby tricorn-like sets" and external rays, and discuss existence of such wiggly features and if "baby tricorn-like sets" are (dynamically) homeomorphic to the tricorn or not.