3 papers
math.DS2026
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 max…
math.DS2025
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…
math.DS2025
Connected McMullen-like Julia sets in a Chebyshev-Halley Family
Jordi Canela, Antonio Garijo, Pascale Roesch
In this paper we study a one parameter family of rational maps obtained by applying the Chebyshev-Halley root finding algorithms. We show that the dynamics near parameters where th…