Dynamics of quadratic polynomials II: rigidity
Mikhail Lyubich
Abstract
This is a continuation of the series of notes on the dynamics of quadratic polynomials. We show the following Rigidity Theorem: Any combinatorial class contains at most one quadratic polynomial satisfying the secondary limbs condition with a-priori bounds. As a corollary, such maps are combinatorially and topologically rigid, and as a consequence, the Mandelbrot set is locally connected at the correspoinding parameter values.
Create a lesson
Related papers
A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations
Floris van Doorn, Polona Durcik, Joris Roos et al.
On some aspects of discrete groups acting ergodically on the boundary
Subhadip Dey, Mikołaj Frączyk, Sebastian Hurtado
A Structural Theory of Admissible Transitions in Biological Reaction Networks
Stephan Peter, Bashar Ibrahim
Sequential and distributive dual futile cycle: Hopf bifurcation can occur under parameter-rich kinetics but cannot occur under mass action kinetics
Nicola Vassena
Rigidity on the two-torus and Sarnak's conjecture
Yinshan Chang, Jian Wang, Junchang Zhou
Linear response for random systems with a cusp
Davrbek Oltiboev, Karim Rakhimov, Marks Ruziboev