Related papers: The solar Julia sets of basic quadratic Cremer pol…
We find an abundance of Cremer Julia sets of an arbitrarily high computational complexity.
For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials $\{P_n\}$ to properties of the support. More precisely we relate the Julia…
In this paper we explore by means of the method of Lagrangian descriptors the Julia sets arising from complex maps, and we analyze their underlying dynamics. In particular, we take a look at two classical examples: the quadratic mapping…
A small perturbation of a quadratic polynomial with a non-repelling fixed point gives a polynomial with an attracting fixed point and a Jordan curve Julia set, on which the perturbed polynomial acts like angle doubling. However, there are…
Laminations are a combinatorial and topological way to study Julia sets. Laminations give information about the structure of parameter space of degree $d$ polynomials with connected Julia sets. We first study fixed point portraits in…
In this paper, we study the large scaled geometric structure of Julia sets of entire and meromorphic functions. Roughly speaking, the structure gives us some asymptotic information about the Julia set near the essential singularity. We will…
Let $f$ be a quadratic polynomial which has an irrationally indifferent fixed point $\alpha$. Let $z$ be a biaccessible point in the Julia set of $f$. Then: 1. In the Siegel case, the orbit of $z$ must eventually hit the critical point of…
In this paper we explore a class of quadratic polynomials having Siegel disks with unbounded type rotation numbers. We prove that any boundary point of Siegel disks of these polynomials is a Lebesgue density point of their filled-in Julia…
For any polynomial map with a single critical point, we prove that its lower Lyapunov exponent at the critical value is negative if and only if the map has an attracting cycle. Similar statement holds for the exponential maps and some other…
We give an introduction to buried points in Julia sets and a list of questions about buried points, written to encourage aficionados of topology and dynamics to work on these questions.
The no invariant line fields conjecture is one of the main outstanding problems in traditional complex dynamics. In this paper we consider non-autonomous iteration where one works with compositions of sequences of polynomials with suitable…
We study the correspondence between unicritical laminations and maximally critical laminations with rotational and identity return polygons. Laminations are a combinatorial and topological way to study Julia sets. Laminations give…
This article deals with the question of local connectivity of the Julia set of polynomials and rational maps. It essentially presents conjectures and questions.
We show that under the definition of computability which is natural from the point of view of applications, there exist non-computable quadratic Julia sets.
Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can be approximated by the basins of attraction of rational…
We relate periodic and recurrent points in dendritic Julia sets. This generalizes well-known results for interval dynamics.
Since the 1980s, much progress has been done in completely determining which functions share a Julia set. The polynomial case was completely solved in 1995, and it was shown that the symmetries of the Julia set play a central role in…
In this paper we shall show that there exists L_0 such that for each even integer L >= L_0 there exists $c_1 \in \rz$ for which the Julia set of $z --> z^L + c_1$ has positive Lebesgue measure. This solves an old problem. Editor's note: In…
We prove that every transcendental meromorphic map f with a disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending…
For quadratic polynomials with an indifferent fixed point with bounded type rotation number (they have a Siegel disk), much of what is known of their Julia set comes from the study of a quasiconformal model. The model is build from a…