2 papers
math.DS2023
Non-degeneracy of closed orbits for generic potentials
Patrick Bernard
We prove that Ma{ñ}{é} generic convex Hamiltonians have only non-degenerate periodic orbits on a given energy level. This result was stated, but not proved, in the literature.
math.DS2023
The Siegel-Bruno linearization Theorem
Patrick Bernard
The purpose of this paper is to provide a short and self-contained account on Siegel's Theorem, as improved by Bruno, which states that a holomorphic map f of C which fixes 0 can b…