Title: Quadratic polynomials and combinatorics of the principal nest

Authors: Rodrigo A Perez

Issue: Volume 54 (2005), Issue 6, 1661-1696

Abstract: We supplement the definition of principal nest, introduced by M. Lyubich, with a "system of frames" that makes possible the classification of combinatorial types for every level of the nest. As a consequence, we give necessary and sufficient conditions for the admissibility of a type and prove that given a sequence of finite admissible types, there is a quadratic polynomial whose nest realizes the sequence.