8 papers · 1 filter
Upper bounds for the moduli of polynomial-like maps
Alexander Blokh, Lex Oversteegen, Vladlen Timorin
We establish a version of the Pommerenke-Levin-Yoccoz inequality for the modulus of a polynomial-like restriction of a global polynomial and give two applications. First it is show…
Symmetric Cubic Laminations
Alexander Blokh, Lex Oversteegen, Nikita Selinger +2
To investigate the degree connectedness locus, Thur\-ston studied \emph{-invariant laminations}, where is the -tupling map on the unit circle, and built a topolog…
Monotonicity of the over-rotation intervals for bimodal maps
Sourav Bhattacharya, Alexander Blokh
We show that the connectedness of the set of parameters for which the over-rotation interval of a bimodal interval map is constant. In other words, the over-rotation interval is a…
Immediate renormalization of complex polynomials
Alexander Blokh, Lex Oversteegen, Vladlen Timorin
A cubic polynomial with a non-repelling fixed point is said to be \emph{immediately renormalizable} if there exists a (connected) quadratic-like invariant filled Julia set…
Unicritical Laminations
Sourav Bhattacharya, Alexander Blokh, Dierk Schleicher
Thurston introduced \emph{invariant (quadratic) laminations} in his 1984 preprint as a vehicle for understanding the connected Julia sets and the parameter space of quadratic polyn…
Cutpoints of invariant subcontinua of polynomial Julia sets
Alexander Blokh, Lex Oversteegen, Vladlen Timorin
We prove fixed point results for branched covering maps of the plane. For complex polynomials with Julia set these imply that periodic cutpoints of some invariant sub…