Date:	Mon, February 18, 2013
Time:	17:15
Place:	Research II Lecture Hall

Abstract: It is well-known that the Mandelbrot set has self-similarity. The tricorn is the corresponding object for the family of anti-holomorphic quadratic polynomials. Hubbard and Schleicher proved that the tricorn is not path connected; such phenomena, which can be easily seen in numerical pictures, strongly suggests that the tricorn does not have such self-similarity as the Mandelbrot set.

With help of rigorous numerical computation, we prove that there exists a "baby tricorn-like set" which is not (dynamically) homeomorphic to the tricorn. We would also discuss the family of real cubic polynomials and the tricorn-like set found by Milnor in this family.