6 papers
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…
A model of the cubic connectedness locus
Alexander Blokh, Lex Oversteegen, Vladlen Timorin
We construct a model of the cubic connectedness locus.
Over-rotation intervals of bimodal interval maps
Sourav Bhattacharya, Alexander Blokh
We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given…