5 papers
Polynomial skew products with small relative degree
Romain Dujardin, Charles Favre, Matteo Ruggiero
We investigate the local dynamics of a proper superattracting holomorphic germ in possessing a totally invariant line such that with $d\ge 2…
Blow-up of multipliers in meromorphic families of rational maps
Charles Favre
We study the blow-up of the multipliers of periodic cycles in one-parameter holomorphic degenerating families of rational maps of the Riemann sphere.
Rigidité, expansion et entropie en dynamique non-archimédienne (Rigidity, expansion and entropy in non-Archimedean dynamics)
Charles Favre, Juan Rivera-Letelier
We prove a rigidity property in non-Archimedean dynamics, reminiscent of Zdunik theorem in complex dynamics: every rational map whose equilibrium measure charges an interval in the…
On the dynamical Manin-Mumford conjecture for plane polynomial maps
Romain Dujardin, Charles Favre, Matteo Ruggiero
We prove the dynamical Manin-Mumford conjecture for regular polynomial maps of A^2 and irreducible curves avoiding super-attracting orbits at infinity, over any field of characteri…
Countability properties of some Berkovich spaces
C. Favre
We prove that any compact Berkovich space over the field of Laurent series over an arbitrary field is angelic. In particular, is it sequentially compact.