6 citations · 16 across the 11 of their papers we have counts for
12 papers
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…
A short ODE proof of the Fundamental Theorem of Algebra
Ramona Anton, Nicolae Mihalache, François Vigneron
We propose a short proof of the Fundamental Theorem of Algebra based on the ODE that describes the Newton flow and the fact that the value is a Lyapunov function. It clari…
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…
Fast Evaluation of Real and Complex Polynomials
Ramona Anton, Nicolae Mihalache, François Vigneron
We propose an algorithm for quickly evaluating polynomials. It pre-conditions a complex polynomial of degree in time , with a low multiplicative constant indepe…
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…