3 citations · 6 across the 12 of their papers we have counts for
14 papers
Biggest bounded type Siegel disks of monic polynomials include those that stick to all critical points
Xavier Buff, Arnaud Chéritat, Pascale Roesch
We prove that for all degree and all bounded type irrational , in the space of monic polynomials having a period Siegel disk of rotation number , the maximu…
Some invariant classes for parabolic renormalization in the multicritical case
Arnaud Chéritat, Pascale Roesch
Parabolic renormalization associates to a holomorphic map f with a parabolic fixed point another holomorphic map with a parabolic fixed point. This procedure is essential for under…
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…
Observations on the hex clusters of the Spectre tilings
Arnaud Chéritat
Decorating the Spectre tile with hexagons reveals triangular hexagonal clusters whose structure we study. In the process we reprove that the Spectre tilings exist and are uniquely…
Similarity surfaces, connections, and the measurable Riemann mapping theorem
Arnaud Chéritat, Guillaume Tahar
This article studies a particular process that approximates solutions of the Beltrami equation (straightening of ellipse fields, a.k.a. measurable Riemann mapping theorem) on $\mat…
Horn maps of holomorphic functions locally pseudo-conjugate on their parabolic basins
Arnaud Chéritat, Dimitri Le Meur
The lifted horn map of a holomorphic function with a simple parabolic point is well known to be a complete local conjugacy invariant; this is a classical result proved independentl…