63 citations · 176 across the 10 of their papers we have counts for
11 papers · 1 filter
On the Shroer-Sauer-Ott-Yorke predictability conjecture for time-delay embeddings
Krzysztof Barański, Yonatan Gutman, Adam Śpiewak
Shroer, Sauer, Ott and Yorke conjectured in 1998 that the Takens delay embedding theorem can be improved in a probabilistic context. More precisely, their conjecture states that if…
On the dimension of points which escape to infinity at given rate under exponential iteration
Krzysztof Barański, Bogusława Karpińska
We prove a number of results concerning the Hausdorff and packing dimension of sets of points which escape (at least in average) to infinity at a given rate under non-autonomous it…
A probabilistic Takens theorem
Krzysztof Barański, Yonatan Gutman, Adam Śpiewak
Let be a Borel set, a Borel probability measure on and a Lipschitz and injective map. Fix greater than the (Hausdorf…
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…
Connectivity of Julia sets of Newton maps: A unified approach
Krzysztof Barański, Núria Fagella, Xavier Jarque +1
In this paper we give a unified proof of the fact that the Julia set of Newton's method applied to a holomorphic function of the complex plane (a polynomial of degree large than $1…
Accesses to infinity from Fatou components
Krzysztof Barański, Núria Fagella, Xavier Jarque +1
We study the boundary behaviour of a meromorphic map on its invariant simply connected Fatou component . To this aim, we develop the theor…
On the dimension of the graph of the classical Weierstrass function
Krzysztof Barański, Balázs Bárány, Julia Romanowska
This paper examines dimension of the graph of the famous Weierstrass non-differentiable function \[ W_{λ, b} (x) = \sum_{n=0}^{\infty}λ^n\cos(2πb^n x) \] for an integer a…
Brushing the hairs of transcendental entire functions
Krzysztof Barański, Xavier Jarque, Lasse Rempe
Let f be a hyperbolic transcendental entire function of finite order in the Eremenko-Lyubich class (or a finite composition of such maps), and suppose that f has a unique Fatou com…
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…