LA was associated with a shorter length of stay and did not compromise the long-term oncological outcome of patients operated on for stage I/II ACC ≤ 10 cm ACC. Our results suggest that LA can be safely proposed to patients with potentially malignant adrenal lesions smaller than 10 cm and without evidence of extra-adrenal extension.
We prove that Misiurewicz parameters with prescribed combinatorics and hyperbolic parameters with (d − 1) distinct attracting cycles with given multipliers are equidistributed with respect to the bifurcation measure in the moduli space of degree d complex polynomials. Our proof relies on Yuan's equidistribution results of points of small heights, and uses in a crucial way Epstein's transversality results.
In the moduli space M d of degree d rational maps, the bifurcation locus is the support of a closed (1, 1) positive current T bif which is called the bifurcation current. This current gives rise to a measure µ bif := (T bif ) 2d−2 whose support is the seat of strong bifurcations. Our main result says that supp(µ bif ) has maximal Hausdorff dimension 2(2d − 2). As a consequence, the set of degree d rational maps having 2d − 2 distinct neutral cycles is dense in a set of full Hausdorff dimension.1.2. Acknowledgment. The author would very much like to thank François Berteloot for his help and encouragement for writting this article. The author also wants to thank Romain Dujardin for his helpful comments and for suggesting Lemma 8.2 and the formulation of Theorem 6.2. Finally, we would like to thank the Referees for their very useful suggestions, which have greatly improved the readability of this work.
The framework2.1. Hyperbolic sets.Definition 2.1. Let f ∈ Rat d and E ⊂ P 1 be a compact f -invariant set, i.e. such that f (E) ⊂ E. We say that E is f -hyperbolic if one of the following equivalent conditions is satisfied:(1) there exists constants C > 0 and α > 1 such that |(f n ) ′ (z)| ≥ Cα n for all z ∈ E and all n ≥ 0, (2) for some appropriate metric on P 1 , there exists K > 1 such that |f ′ (z)| ≥ K for all z ∈ E. One says that K is the hyperbolicity constant of E.The following Theorem is now classical (see [dMvS] Theorem 2.3 page 225 or [Sh] section 2 for a sketch of proof):Theorem 2.2 (de Melo-van Strien). Let (f λ ) λ∈B(0,r) be a holomorphic family of degree d rational maps parametrized by a ball B(0, r) ⊂ C m . Let E 0 ⊂ P 1 be a compact f 0 -hyperbolic set. Then there exists 0 < ρ ≤ r and a unique holomorphic motion
We describe all special curves in the parameter space of complex cubic polynomials, that is all algebraic irreducible curves containing infinitely many post-critically finite polynomials. This solves in a strong form a conjecture by Baker and DeMarco for cubic polynomials.Let Perm(λ) be the algebraic curve consisting of those cubic polynomials that admit an orbit of period m and multiplier λ. We also prove that an irreducible component of Perm (λ) is special if and only if λ = 0.
Given a sequence of complex numbers ρ n , we study the asymptotic distribution of the sets of parameters c ∈ C such that the quadratic map z 2 + c has a cycle of period n and multiplier ρ n . Assume 1 n log |ρ n | → L. If L ≤ log 2, they equidistribute on the boundary of the Mandelbrot set. If L > log 2, they equidistribute on the equipotential outside the Mandelbrot set of level 2L − 2 log 2.We denote by K c the filled-in Julia set of f c and by J c the Julia set:The Mandelbrot set M is the set of parameters c ∈ C such that 0 ∈ K c .
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