17 citations · 63 across the 15 of their papers we have counts for
19 papers
On the dimension of the boundaries of attracting basins of entire maps
Krzysztof Barański, Bogusława Karpińska, David Martí-Pete +2
Let be a transcendental entire map from the Eremenko-Lyubich class , and let be an attracting periodic point of period . We…
Asymptotics of the Hausdorff measure for the Gauss map and its linearized analogue
Rafał Tryniecki, Mariusz Urbański, Anna Zdunik
Let be the Gauss map. By we denote its continuous/real analytic inverse branches. We define iterated function system (IFS) by limiting…
Equilibrium measures on Julia sets of random quadratic polynomials
Krzysztof Lech, Anna Zdunik
We consider sequences of compositions of quadratic polynomials . For such sequences one can naturally generalize the definitions of the Julia set and basin…
Total disconnectedness of Julia sets of random quadratic polynomials
Krzysztof Lech, Anna Zdunik
For a sequence of complex parameters we consider the compositions of functions , which is the non-autonomous version of the classical quadratic d…
On Hausdorff dimension of polynomial not totally disconnected Julia sets
Feliks Przytycki, Anna Zdunik
We prove that for every polynomial of one complex variable of degree at least 2 and Julia set not being totally disconnected nor a circle, nor interval, Hausdorff dimension of this…
Thermodynamic formalism for coarse expanding dynamical systems
Tushar Das, Feliks Przytycki, Giulio Tiozzo +2
We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discuss…
The failure of Ruelle's property for entire functions
Volker Mayer, Anna Zdunik
We exhibit an analytic family of hyperbolic, even disjoint type, entire functions for which the hyperbolic dimension does not vary analytically. Additionally we answer several ques…
Random non-hyperbolic exponential maps
Mariusz Urbański, Anna Zdunik
We consider random iteration of exponential entire functions, i.e. of the form , . Assuming that $…
The Central Limit Theorem for function systems on the circle
Tomasz Szarek, Anna Zdunik
The Central Limit Theorem for Iterated Functions Systems on the circle is proved. We study also ergodicity of such systems.
Stability of iterated function systems on the circle
Tomasz Szarek, Anna Zdunik
We prove that any Iterated Function System of circle homeomorphisms with at least one of them having dense orbit, is asymptotically stable. The corresponding Perron-Frobenius opera…
Conformal measures for meromorphic maps
Krzysztof Barański, Bogusława Karpińska, Anna Zdunik
In this paper we study the relation between the existence of a conformal measure on the Julia set of a transcendental meromorphic map and the existence of zero of the to…
Thin annuli property and exponential distribution of return times for Weakly Markov systems
Łukasz Pawelec, Mariusz Urbański, Anna Zdunik
We deal with the problem of asymptotic distribution of first return times to shrinking balls under iteration generated by a large general class of dynamical systems called weakly M…
Real Analyticity for random dynamics of transcendental functions
Volker Mayer, Mariusz Urbanski, Anna Zdunik
Analyticity results of expected pressure and invariant densities in the context of random dynamics of transcendental functions are established. These are obtained by a refinement o…
Indecomposable continua in exponential dynamics-Hausdorff dimension
Lukasz Pawelec, Anna Zdunik
We study some forward invariant sets appearing in the dynamics of the exponential family. We prove that the Hausdorff dimension of the sets under consideration is not larger than $…
Hausdorff and harmonic measures on non-homogeneous Cantor sets
Athanasios Batakis, Anna Zdunik
We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smalle…
Bowen's formula for meromorphic functions
Krzysztof Barański, Bogusława Karpińska, Anna Zdunik
Let be an arbitrary transcendental entire or meromorphic function in the class (i.e. with finitely many singularities). We show that the topological pressure $P(f,…
Dimension properties of the boundaries of exponential basins
Krzysztof Barański, Bogusława Karpińska, Anna Zdunik
We prove that the boundary of a component of the basin of an attracting periodic cycle (of period greater than 1) for an exponential map on the complex plane has Hausdorff dime…
Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts
Krzysztof Barański, Bogusława Karpińska, Anna Zdunik
We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class ), the Julia set contains a compact…
Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps, geometric coding trees technique
Feliks Przytycki, Anna Zdunik
We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, then periodic points in the boundary…