5 papers
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…
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 $…
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…
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…