5 papers
On the MLC Conjecture and the Renormalization Theory in Complex Dynamics
Dzmitry Dudko
In this Note, we present recent developments in the Renormalization Theory of quadratic polynomials and discuss their applications, with an emphasis on the MLC conjecture, the prob…
MLC at Feigenbaum points
Dzmitry Dudko, Mikhail Lyubich
We prove a priori bounds for Feigenbaum quadratic polynomials, i.e., infinitely renormalizable polynomials of bounded type. It implies local connectivity of t…
Correspondences on Riemann surfaces and non-uniform hyperbolicity
Laurent Bartholdi, Dzmitry Dudko, Kevin M. Pilgrim
We consider certain correspondences on a Riemann surface, and show that they admit a weak form of hyperbolicity: sufficiently long loops get shorter under lifting at a fixed point…
Uniform a priori bounds for neutral renormalization. Variation II: -ql Siegel maps
Dzmitry Dudko, Yusheng Luo, Mikhail Lyubich
We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to -quadratic-like Siegel maps. In this form, the bounds are compatible with the -quadratic…
Uniform a priori bounds for neutral renormalization
Dzmitry Dudko, Mikhail Lyubich
We prove uniform ``pseudo-Siegel'' a priori bounds for Siegel disks of bounded type that give a uniform control of oscillations of their boundaries in all scales. As a consequence,…