4 papers · 1 filter
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…