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Dynamics of complex quadratic polynomials with an irrationally indifferent fixed point

Davoud Cheraghi
University of Warwick

Ergodic Theory and Dynamical Systems

Organisers: Andrew Ferguson, Thomas Jordan

ABSTRACT
An irrationally indifferent fixed point of a quadratic polynomial is a fixed point at which the multiplier of the map has absolute value one and irrational argument. In this talk we study the dynamics of quadratic polynomials with such fixed points on the complex plane.

To this end, we briefly introduce a renormalization technique due to H. Inou and M. Shishikura and show how it may be used to analyze the dynamics of such quadratic maps. The talk should be self contained and does not assume any knowledge of complex dynamics.