Rodrigo Perez (SUNY Stony Brook)

Finite recurrence patterns in the quadratic family.

Abstract. The principal nest is a collection of pieces in the Yoccoz puzzle of a Julia set. It encodes properties of the critical orbit that may imply strong geometric results like local connectivity and hairiness. In the talk we endow the principal nest with extra structure that completely determines the combinatorial class of the map. One important consequence is a complete characterization of complex quadratic Fibonacci maps. This is done as a particular case of a large family of examples with simple recurrence.