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math.DS2022
Speiser meets Misiurewicz
Magnus Aspenberg, Weiwei Cui
We propose a notion of Misiurewicz condition for transcendental entire functions and study perturbations of Speiser functions satisfying this condition in their parameter spaces (i…
math.DS2022
Slowly recurrent Collet-Eckmann maps with non-empty Fatou set
Magnus Aspenberg, Mats Bylund, Weiwei Cui
In this paper we study rational Collet-Eckmann maps for which the Julia set is not the whole sphere and for which the critical points are recurrent at a slow rate. In families wher…
math.DS2022
Perturbations of exponential maps: Non-recurrent dynamics
Magnus Aspenberg, Weiwei Cui
We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that…