6 citations · 12 across the 6 of their papers we have counts for
8 papers
Irreducibility of periodic curves in cubic polynomial moduli space
Matthieu Arfeux, Jan Kiwi
In the moduli space of complex cubic polynomials with a marked critical point, given any p>=1, we prove that the loci formed by polynomials with the marked critical point periodic…
Irreducibility of the set of cubic polynomials with one periodic critical point
Matthieu Arfeux, Jan Kiwi
The space of monic centered cubic polynomials with marked critical points is isomorphic to C^2. For each n>0, the locus Sn formed by all polynomials with a specified critical point…
Arbitrary large number of non trivial rescaling limits
Matthieu Arfeux, Guizhen Cui
We construct a family of rational map sequences providing an arbitrary large number of dynamically independent rescaling limits of non monomial type. From this, we deduce the exist…
Berkovich spaces and Deligne-Mumford compactification
Matthieu Arfeux
We explicit the relation between the dynamics the Berkovich projective line over the completion of the field of formal Puiseux series and the space dynamical systems between trees…
Reading escaping trees from Hubbard trees in Sn
Matthieu Arfeux
We prove that the parameter space of monic centered cubic polynomials with a critical point of exact period n=4 is connected. The techniques developed for this proof work for every…
Approximability of dynamical systems between trees of spheres
Matthieu Arfeux
We study sequences of analytic conjugacy classes of rational maps which diverge in moduli space. In particular, we are interested in the notion of rescaling limits introduced by Ja…