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math.DS2020
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…
math.DS2019
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…
math.DS2018
Random non-hyperbolic exponential maps
Mariusz Urbański, Anna Zdunik
We consider random iteration of exponential entire functions, i.e. of the form , . Assuming that $…