8 citations · 19 across the 6 of their papers we have counts for
6 papers
Some connections of complex dynamics
Alexandre DeZotti
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but…
Dimension paradox of irrationally indifferent attractors
Davoud Cheraghi, Alexandre DeZotti, Fei Yang
We prove that for an infinite dimensional class of holomorphic maps with an elliptic fixed point, the post-critical set has Hausdorff dimension two, provided the rotation number is…
Eventual hyperbolic dimension of entire functions and Poincaré functions of polynomials
Alexandre DeZotti, Lasse Rempe-Gillen
Let be an entire function. A Poincaré function of is the entire extension of a linearising coord…
Convergence properties of the Gronwall area formula for quadratic Julia sets
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 approximate…
On (non-)local-connectivity of some Julia sets
Alexandre Dezotti, Pascale Roesch
This article deals with the question of local connectivity of the Julia set of polynomials and rational maps. It essentially presents conjectures and questions.
Connectedness of the Arnold tongues for double standard maps
Alexandre Dezotti
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 m…