18 citations · 49 across the 11 of their papers we have counts for
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math.DS2012
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…
math.DS2012★ 18 cited
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…
math.DS2012★ 7 cited
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…