3 papers
math.DS2000
A note on holomorphic extensions
Ricardo Perez-Marco
We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functio…
math.DS2000
Linearization of holomorphic germs with resonant linear part
Ricardo Perez-Marco
We study the linearization problem of germs of holomorphic diffeomorphisms with resonant linear part. The formal linearization requires in general an infinite number of algebraic r…
math.DS2000
Convergence or generic divergence of Birkhoff normal form
Ricardo Perez-Marco
We prove that Birkhoff normal form of hamiltonian flows at a non-resonant singular point with given quadratic part are always convergent or generically divergent. The same result i…