Brjuno and Rüssmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sharp for quadratic ...

The Schwarz lemma stands as a cornerstone result in complex analysis, constraining holomorphic self-mappings of the unit disc by bounding both their magnitude and derivative. Traditionally, it affirms ...

One of the fundamental questions in holomorphic dynamics is understanding the behavior of a dynamical system in the neighborhood of a fixed point. In dimension one, this question has been extensively ...