arXiv subjects
Publications and source records attributed to Alexandre Dezotti.
Using parabolic enrichment, it is shown that Gronwall area formula for the filled Julia set along the boundary of the main cardioid of the Mandelbrot set cannot be well approximated by replacing it by a finite sum. A revised version of this article will appear in the Journal of the London Mathematical Society.
This article deals with the question of local connectivity of the Julia set of polynomials and rational maps. It essentially presents conjectures and questions.
We show that the Arnold tongues of the family of double standard maps f_{a,b}(x) = 2x + a + (b/pi) sin(2 pi x), are connected. This proof is accomplished in the complex domain by means of quasiconformal techniques and depends partly upon the fact that the complexification of f_{a,b} has only one critical point taking symmetry into account.