17 citations · 38 across the 7 of their papers we have counts for
10 papers
Models for spaces of dendritic polynomials
Alexander Blokh, Lex Oversteegen, Ross Ptacek +1
Complex 1-variable polynomials with connected Julia sets and only repelling periodic points are called \emph{dendritic}. By results of Kiwi, any dendritic polynomial is semi-conjug…
The combinatorial Mandelbrot set as the quotient of the space of geolaminations
A. Blokh, L. Oversteegen, V. Timorin +1
We interpret the combinatorial Mandelbrot set in terms of \it{quadratic laminations} (equivalence relations on the unit circle invariant under ). To each lamination we…
The parameter space of cubic laminations with a fixed critical leaf
Alexander Blokh, Lex Oversteegen, Ross Ptacek +1
Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward…
Complementary components to the cubic Principal Hyperbolic Domain
Alexander Blokh, Lex Oversteegen, Ross Ptacek +1
We study the closure of the cubic Principal Hyperbolic Domain and its intersection with the slice of the space of all cubic polynomials with fixed p…
Combinatorial models for spaces of cubic polynomials
Alexander Blokh, Lex Oversteegen, Ross Ptacek +1
A model for the Mandelbrot set is due to Thurston and is stated in the language of geodesic laminations. The conjecture that the Mandelbrot set is actually homeomorphic to this mod…
Laminational models for some spaces of polynomials of any degree
Alexander Blokh, Lex Oversteegen, Ross Ptacek +1
The so-called "pinched disk" model of the Mandelbrot set is due to A.~Douady, J.~H.~Hubbard and W.~P.~Thurston. It can be described in the language of geodesic laminations. The com…