Slowly recurrent ColletEckmann maps with nonempty Fatou set
Abstract
In this paper we study rational ColletEckmann 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 where the orders of the critical points are fixed, we prove that such maps are Lebesgue density points of hyperbolic maps. In particular, if all critical points are simple, they are Lebesgue density points of hyperbolic maps in the full space of rational maps of any degree $d \geq 2$.
 Publication:

arXiv eprints
 Pub Date:
 July 2022
 DOI:
 10.48550/arXiv.2207.14046
 arXiv:
 arXiv:2207.14046
 Bibcode:
 2022arXiv220714046A
 Keywords:

 Mathematics  Dynamical Systems;
 37F10;
 37F15;
 30D05
 EPrint:
 Proc. Lond. Math. Soc. (3) 128 (2024), no. 1, Paper No. e12574, 32 pp