Analytic structures and harmonic measure at bifurcation locus

Graczyk, Jacek; Świątek, Grzegorz

doi:10.1016/j.aim.2023.108998

Cited by 1 publication

(2 citation statements)

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“…M. Benedicks and J. Graczyk also have a preprint (unpublished) on perturbations on such (quadratic or, more generally, unicritical) maps. The maps there and in the recent papers [14,15] are also slowly recurrent, and hence the results in this paper are partially a generalisation of some of those results. We will not use a harmonic measure, but develop the classical Benedicks-Carleson parameter exclusion techniques and combine it with strong results on transversality, by G. Levin [18].…”

Section: Introductionsupporting

confidence: 72%

“…We are going to study perturbations of such maps in the complex setting. For the quadratic family and other unicritical families, J. Graczyk and G. Świaţek recently made an extensive study of perturbations of typical Collet-Eckmann maps with respect to harmonic measure, in a series of papers [12][13][14][15]. M. Benedicks and J. Graczyk also have a preprint (unpublished) on perturbations on such (quadratic or, more generally, unicritical) maps.…”

Section: Introductionmentioning

confidence: 99%

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Slowly recurrent Collet–Eckmann maps with non‐empty Fatou set

Aspenberg,

Bylund,

Cui

2023

Proceedings of London Math Soc

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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 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, these maps are Lebesgue density points of hyperbolic maps in the full space of rational maps of any degree .

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Section: Introductionsupporting

confidence: 72%