Dynamics of quadratic polynomials, I: Combinatorics and geometry of the Yoccoz puzzle

1995/03/01 by Lyubich, Mikhail
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/9503215

Abstract

This work studies combinatorics and geometry of the Yoccoz puzzle for quadratic polynomials. It is proven that the moduli of the ``principal nest'' of annuli grow at linear rate. As a corollary we obtain complex a priori bounds and local connectivity of the Julia set for many infinitely renormalizable quadratics.

Related

• The Renormalization Method and Quadratic-Like Maps
• The dual nest for degenerate Yoccoz puzzles
• Dynamics of quadratic polynomials: Complex bounds for real maps
• Geometry of quadratic polynomials: moduli, rigidity and local connectivity
• Topology of the regular part for infinitely renormalizable quadratic polynomials