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math.DS2022
A parameter ASIP for the quadratic family
Magnus Aspenberg, Viviane Baladi, Tomas Persson
Consider the quadratic family , for and mixing Collet--Eckmann (CE) parameters . For bounded , set $\tilde φ_{a} := φ- \int φ\,…
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…