Related papers: A non-laminar dynamical Green current

Let F: P^N_K --> P^N_K be a morphism of degree d > 1 defined over a field K that is algebraically closed and complete with respect to a nonarchimedean absolute value. We prove that a modified Green function G_F associated to F is Holder…

A hyperbolic transcendental entire function with connected Fatou set is said to be "of disjoint type". It is known that a disjoint-type function provides a model for the dynamics near infinity of all maps in the same parameter space; hence…

We present a number of rigidity results concerning holomorphic dynamical systems admitting rotation quasicircles. Firstly, we show the absence of line fields on the Julia set of any rational map that is geometrically finite away from a…

In holomorphic semigroup dynamics, Julia set is in general backward invariant and so some fundamental results of classical complex dynamics can not be generalized to semigroup dynamics. In this paper, we define completely invariant Julia…

We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. Moreover, we investigate the associated random dynamics of polynomials.…

Let f and g two rational functions having the same Julia set J_f. Lets suppose that f has a rational indifferent periodic point and that the critical set of f is disjoint of J_f. Then or J_f has to be equal to P^1, a circle, an arc of a…

Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…

In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a…

Let $f$ be a polynomial automorphism of ${\Bbb C}^k$ of degree $\lambda$, whose rational extension to ${\Bbb P}^k$ maps the hyperplane at infinity to a single point. Given any positive closed current $S$ on ${\Bbb P}^k$ of bidegree (1,1),…

The goal of this paper is to study some basic properties of the Fatou and Julia sets for a family of holomorphic endomorphisms of $\mathbb{C}^k,\; k \ge 2$. We are particularly interested in studying these sets for semigroups generated by…

Let (F_n) be a sequence of (multivalued) meromorphic maps between compact Kaehler manifolds X1 and X2. We study the asymptotic distribution of preimages of points by F_n and the asymptotic distribution of fixed points for multivalued…

This article gives a precise description of the Fatou sets and Julia sets of matrix-valued polynomials in $\mathcal{M}(2,\mathbb{C})$ in terms of the corresponding polynomials in $\mathbb{C}$. Further, we construct Green functions and…

This article deals with the question of local connectivity of the Julia set of polynomials and rational maps. It essentially presents conjectures and questions.

In this paper we introduce the notion of dynamical systems over the class of the normed real nonassociative algebras not necessarily finite-dimensional, generalize the classical filled Julia and Mandelbrot sets over the complex numbers,…

We prove: If $f(z)$ is a critically finite rational map which has exactly two critical points and which is not conjugate to a polynomial, then the boundary of every Fatou component of $f$ is a Jordan curve. If $f(z)$ is a hyperbolic…

This paper is a continuation of authors work: Fatou and Julia like sets,Ukranian J. Math., to appear/arXiv:2006.08308[math.CV](see [4]). Here, we introduce escaping like set and generalized escaping like set for a family of holomorphic…

We show that Fatou components of a semi-hyperbolic rational map are John domains and that the converse does not hold. This generalizes a famous result of Carleson, Jones and Yoccoz. We show that a connected Julia set is locally connected…

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and…

For a sequence of complex parameters $\{c_n\}$ we consider the compositions of functions $f_{c_n} (z) = z^2 + c_n$, which is the non-autonomous version of the classical quadratic dynamical system. The definitions of Julia and Fatou sets are…

We investigate the dynamics of polynomial semigroups (semigroups generated by a family of polynomial maps on the Riemann sphere) and the random dynamics of polynomials on the Riemann sphere. Combining the dynamics of semigroups and the…