12 citations · 47 across the 14 of their papers we have counts for
15 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…
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…
The Parabolic Mandelbrot Set
Carsten Lunde Petersen, Pascale Roesch
We solve the longstanding conjecture by Milnor (1993) concerning the connectedness locus of the family of quadratic rational maps tangent to the identity at . We prov…
Rigidity of non-renormalizable Newton maps
Pascale Roesch, Yongcheng Yin, Jinsong Zeng
Non-renormalizable Newton maps are rigid. More precisely, we prove that their Julia set carries no invariant line fields and that the topological conjugacy is equivalent to quasi-c…
Julia sets with a wandering branching point
Xavier Buff, Jordi Canela, Pascale Roesch
According to the Thurston No Wandering Triangle Theorem, a branching point in a locally connected quadratic Julia set is either preperiodic or precritical. Blokh and Oversteegen pr…