Quadratic polynomials and combinatorics of the principal nest Rodrigo Perez 37F20complex dynamicsYoccoz puzzleprincipal nest 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. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2730 10.1512/iumj.2005.54.2730 en Indiana Univ. Math. J. 54 (2005) 1661 - 1696 state-of-the-art mathematics http://iumj.org/access/