Filled Julia sets with empty interior are computable
We show that if a polynomial filled Julia set has empty interior, then it is computable.
math.DS↗
arXiv subjects
M. Yampolsky
Publications and source records attributed to M. Yampolsky.
On computational complexity of Siegel Julia sets
It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.
math.DS↗
The rigidity problem for analytic critical circle maps
It is shown that if $f$ and $g$ are any two analytic critical circle mappings with the same irrational rotation number, then the conjugacy that maps the critical point of $f$ to that of $g$ has regularity $C^{1+α}$ at the critical point, with a universal value of $α>0$. As a consequence, a new proof of the hyperbolicity of the full renormalization horseshoe of critical circle maps is given.
math.DS↗