12 citations · 17 across the 15 of their papers we have counts for
19 papers
Versal deformations of vector field singularities
Mauricio Garay, Duco van Straten
When a singular point of a vector field passes through resonance, a formal invariant cone appears. In the seventies, Pyartli proved that for -resonance the cone is in fact…
A Category of Banach Space Functors
Mauricio Garay, Duco van Straten
We introduce a sheaf theoretic viewpoint on functional analysis designed for infinite dimensional Lie group actions. We develop functional calculus for Banach valued functors and,…
KAM THEORY. Part 3. Applications
Mauricio Garay, Duco van Straten
We apply the general normal form theorems in Kolmogorov spaces to three classical cases: deformations of hypersurface singularities, normal forms of vector fields and invariant tor…
KAM Theory. Part II. Kolmogorov spaces
Mauricio Garay, Duco van Straten
This is part II of our book on KAM theory. We start by defining functorial analysis and then switch to the particular case of Kolmogorov spaces. We develop functional calculus base…
KAM Theory. Part I. Group actions and the KAM problem
Mauricio Garay, Duco van Straten
This is part I of a book on KAM theory. We start from basic symplectic geometry, review Darboux-Weinstein theorems action angle coordinates and their global obstructions. Then we e…
Quasi-periodic motions on symplectic tori
Mauricio Garay, Arezki Kessi, Duco van Straten +1
The KAM (Kolmogorov-Arnold-Moser) theorem guarantees the stability of quasi-periodic invariant tori by perturbation in some Hamiltonian systems. Michel Herman proved a similar resu…