Seminars｜Fostering top leaders in mathematics -- broadening the core and exploring new ground

Seminar

Language	English
From	2012/07/13 14:00
To	2012/07/13 17:00
Place	Room 609, Building No.6, Faculty of Science, Kyoto University
Seminar Name	Kyoto Dynamical Systems Seminar
Title	Trajectories of complex quadratic polynomials with an irrationally indifferent fixed point
Field	Analysis Other
Speakers	Davoud Cheraghi
Affiliation	University of Warwick
Abstract	The local, semi-local, and global dynamics of the complex quadratic polynomials $P_\alpha(z):=e^{2\pi i \alpha}z+z^2: \mathbb{C}\to <br>\mathbb{C}$ , for irrational values of $\alpha$ , have been extensively studied through various methods. The main source of difficulty is the interplay between the tangential movement created by the fixed point and the radial movement caused by the critical point. This naturally brings the arithmetic nature of $\alpha$ into play. Using a renormalization technique developed by H. Inou and M. Shishikura, we analyze this interaction, and in particular, describe the topological behavior of the orbit of typical points under these maps.
Link	http://www.math.kyoto-u.ac.jp/dynamics/