5 papers · 1 filter
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…
Dynamics of generic 1-parameter perturbations of a vector field with a singular point of codimension k
Arnaud Chéritat, Chrisitane Rousseau
The paper describes the bifurcation diagram of germs of generic -parameter families of complex vector fields on , unfolding a singular point of m…
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…
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…
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…