6 citations · 16 across the 11 of their papers we have counts for
10 papers · 1 filter
Precise asymptotics at the tip of the Mandelbrot set
Neil Dobbs, Jacek Graczyk, Nicolae Mihalache
For the quadratic family , the only parameters in the Mandelbrot set for which the Julia set has Hausdorff dimension are and . Nea…
On the local connectivity of attractors of Markov IFS
Nicolae Mihalache
We prove an extension of M. Hata's theorem [4] for planar Markov Iterated Function Systems satisfying a strong version of the Open Set Condition. More precisely, if the attractor o…
An invitation to rough dynamics: zipper maps
Benoît Kloeckner, Nicolae Mihalache
In the field of dynamical systems, it is not rare to meet irregular functions, which are typically H{ö}lder but not Lipschitz (e.g. the Weierstrass functions). Our goal is to scrat…
Hausdorff dimension of Julia sets in the logistic family
Neil Dobbs, Jacek Graczyk, Nicolae Mihalache
A closed interval and circle are the only smooth Julia sets in polynomial dynamics. D. Ruelle proved that the Hausdorff dimension of unicritical Julia sets close to the circle depe…
Collet, Eckmann and the bifurcation measure
Matthieu Astorg, Thomas Gauthier, Nicolae Mihalache +1
The moduli space of degree rational maps can naturally be endowed with a measure detecting maximal bifurcations, called the bifurcation me…
Diabolical entropy
Neil Dobbs, Nicolae Mihalache
Milnor and Thurston's famous paper proved monotonicity of the topological entropy for the real quadratic family. Guckenheimer showed that it is Hölder continuous. We obtain a preci…