4 papers
MLC for parabolically bounded primitive renormalization
Jeremy Kahn, Alex Kapiamba, Mikhail Lyubich
We prove bounds and MLC (local connectivity of the Mandelbrot set ) for a class of infinitely renormalizable parameters whose renormalization type…
Non-degenerate near-parabolic renormalization
Alex Kapiamba
Invariant classes under parabolic and near-parabolic renormalization have proved extremely useful for studying the dynamics of polynomials. The first such class was introduced by I…
An optimal Yoccoz inequality for near-parabolic quadratic polynomials
Alex Kapiamba
Using Lavaurs maps and near-parabolic renormalization, we describe the degenerating geometry of external rays for quadratic polynomials when a periodic cycle becomes parabolic. We…
The near-parabolic geometry of external rays
Alex Kapiamba
Using Lavaurs maps and near-parabolic renormalization, we describe the degenerating geometry of external rays for quadratic polynomials when a periodic cycle becomes parabolic. We…