5 papers
The Hamiltonian Normal Form
Mauricio Garay, Duco van Straten
An important step in the proof of the Herman invariant tori conjecture was the introduction of a normal form with poles along the resonance loci, replacing the Birkhoff normal form…
Fixed point theorems for small divisors problems
Mauricio Garay, Duco van Straten
In the seventies', Zehnder found a Nash-Moser type implicit function theorem in the analytic set-up. This theorem has found many applications in dynamical systems although its appl…
A new class of Borel monogenic functions
Mauricio Garay, Duco van Straten
Spaces of quasi-analytic classes are defined by the existence and uniqueness of Taylor expansions, which are not necessarily convergent. First examples were given by Borel in his t…
Non degenerate Birkhoff functions
Mauricio Garay, Duco van Straten
It is known after the works of Mahler, Kleinbock, Margulis, Sprindžuk and others that very well approximated numbers on a manifold form a zero measure set, assuming non-degeneracy…
The Herman invariant tori conjecture
Mauricio Garay, Duco van Straten
We study a new type of normal form at a critical point of an analytic Hamiltonian. Under a Bruno condition on the frequency, we prove a convergence statement to the normal form. Us…