18 citations · 49 across the 11 of their papers we have counts for
13 papers
Cubic Siegel polynomials and the bifurcation measure
Matthieu Astorg, Davoud Cheraghi, Arnaud Chéritat
We prove that cubic polynomial maps with a fixed Siegel disk and a critical orbit eventually landing inside that Siegel disk lie in the support of the bifurcation measure. This ans…
Arithmetic geometric model for the renormalisation of irrationally indifferent attractors
Davoud Cheraghi
In this paper we build a geometric model for the renormalisation of irrationally indifferent fixed points. The geometric model incorporates the fine arithmetic properties of the ro…
Analytic maps of parabolic and elliptic type with trivial centralisers
Artur Avila, Davoud Cheraghi, Alexander Eliad
We prove that for a dense set of irrational numbers , the analytic centraliser of the map near is trivial. We also prove that some analytic circle diffeom…
Lacunary series, resonances, and automorphisms of with a round Siegel domain
Davoud Cheraghi, Francois Berteloot
We construct transcendental automorphims of having an unbounded and regular Siegel domain.
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…
Hairy Cantor sets
Davoud Cheraghi, Mohammad Pedramfar
We introduce a topological object, called hairy Cantor set, which in many ways enjoys the universal features of objects like Jordan curve, Cantor set, Cantor bouquet, hairy Jordan…
Topology of irrationally indifferent attractors
Davoud Cheraghi
We study the post-critical set of a class of holomorphic systems with an irrationally indifferent fixed point. We prove a trichotomy for the topology of the post-critical set based…
Satellite renormalization of quadratic polynomials
Davoud Cheraghi, Mitsuhiro Shishikura
We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on an infinite-dimensional space of holomorphic transformations. This implies the universa…
Statistical properties of quadratic polynomials with a neutral fixed point
Artur Avila, Davoud Cheraghi
We describe the statistical properties of the dynamics of the quadratic polynomials P_a(z):=e^{2πa i} z+z^2 on the complex plane, with a of high return times. In particular, we sho…
A Proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type
Davoud Cheraghi, Arnaud Chéritat
Marmi Moussa and Yoccoz conjectured that some error function Upsilon, related to the approximation of the size of Siegel disk by some arithmetic function of the rotation number the…
Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type
Davoud Cheraghi
We describe the topological behavior of typical orbits of complex quadratic polynomials P_alpha(z)=e^{2πi alpha} z+z^2, with alpha of high return type. Here we prove that for such…
Typical orbits of quadratic polynomials with a neutral fixed point: non-Brjuno type
Davoud Cheraghi
We investigate the quantitative and analytic aspects of the near-parabolic renormalization scheme introduced by Inou and Shishikura in 2006. These provide techniques to study the d…
Combinatorial rigidity for some infinitely renormalizable unicritical polynomials
Davoud Cheraghi
We prove combinatorial rigidity of infinitely renormalizable unicritical polynomials, P_c :z \mapsto z^d+c, with complex c, under the a priori bounds and a certain "combinatorial c…