arXiv subjects

Carsten Lunde Petersen

Publications and source records attributed to Carsten Lunde Petersen.

21 records · Page 2Linked to original sources

arXiv2011

Conformally Natural extensions revisited

In this note we revisit the notion of conformal barycenter of a measure on $\SS^n$ as defined by Douady and Earle in Acta Math. Vol 157, 1986. The aim is to extend rational maps from the Riemann sphere $\Cbar\isom\SS^2$ to the (hyperbolic) three ball $\BB^3$ and thus to $\SS^3$ by reflection. The construction which was pioneered by Douady and Earle in the case of homeomorphisms actually gives extensions for more general maps such as entire transcendental maps on $\C\subset\Cbar$. And it works for maps in any dimension.

math.GT↗

arXiv2010

Carrots for dessert

Carrots for dessert is the title of a section of the paper `On polynomial-like mappings' by Douady and Hubbard. In that section the authors define a notion of dyadic carrot fields of the Mandelbrot set M and more generally for Mandelbrot like families. They remark that such carrots are small when the dyadic denominator is large, but they do not even try to prove a precise such statement. In this paper we formulate and prove a precise statement of asymptotic shrinking of dyadic Carrot-fields around M. The same proof carries readily over to show that the dyadic decorations of copies M' of the Mandelbrot set M inside M and inside the parabolic Mandelbrot set shrink to points when the denominator diverge to infinity.

math.DS↗

arXiv2009

Polynomial-like semi-conjugates of the shift map

In this paper I prove that for a polynomial of degree $d$ with a Cantor Julia set $J$, the Julia set can be understood as the simplest possible quotiont of the one sided shift space $Σ_d$ with dynamics given by the shift. Here simplest possible means that, the projection $π: Σ_d \Rightarrow J$ is as injective as possible.

math.DS↗