arXiv subjects

Krzysztof Barański

Publications and source records attributed to Krzysztof Barański.

20 records · Page 2Linked to original sources

arXiv2009

Dimension properties of the boundaries of exponential basins

We prove that the boundary of a component $U$ of the basin of an attracting periodic cycle (of period greater than 1) for an exponential map on the complex plane has Hausdorff dimension greater than 1 and less than 2. Moreover, the set of points in the boundary of $U$ which do not escape to infinity has Hausdorff dimension (in fact: hyperbolic dimension) greater than 1, while the set of points in the boundary of $U$ which escape to infinity has Hausdorff dimension 1.

math.DS↗

arXiv2007

Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts

We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class $\mathcal B$), the Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff dimension greater than 1. Hence, the hyperbolic dimension of the Julia set is greater than 1.

math.DS↗