Arnaud Chéritat

collaborators

5 papers

math.DS2026

Biggest bounded type Siegel disks of monic polynomials include those that stick to all critical points

Xavier Buff, Arnaud ChÃ©ritat, Pascale Roesch

We prove that for all degree $d \geq 2$ and all bounded type irrational $I^¸$ , in the space of monic polynomials having a period $1$ Siegel disk $I^$ of rotation number $I^¸$ , the max…

math.DS2026

Dynamics of generic 1-parameter perturbations of a vector field with a singular point of codimension k

Arnaud ChÃ©ritat, Chrisitane Rousseau

The paper describes the bifurcation diagram of germs of generic $1$ -parameter families of complex vector fields $z ˙ = I ¨ _{I^} µ (z)$ on $C$ , unfolding a singular point of m…

math.DS2025

Some invariant classes for parabolic renormalization in the multicritical case

Arnaud ChÃ©ritat, 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…

math.CV2025

Similarity surfaces, connections, and the measurable Riemann mapping theorem

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…

math.DS2025

Horn maps of holomorphic functions locally pseudo-conjugate on their parabolic basins

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…