**abstract:**
A fixed point of a holomorphic mapping of one variable is called irrationally indifferent if the derivative (multiplier) has modulus one without being a root of unity. It has been known that such a fixed point leads to a complicated invariant set especially when the fixed point is not linearizable. We focus on the case where the rotation number is of high type (the continued fraction expansion has large coefficients), and analyze the dynamics via near-parabolic renormalization. For a certain class of maps, including quadratic polynomials, we give a description of invariant sets around the fixed point and prove that when the map is linearizable, the boundary of Siegel disk (the maximal domain of linearization) is always a Jordan curve.

Wed 14 Oct, 9:00 - 10:00, Aula Dini

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