3 papers
math.DS2025
Singular KAM theory for convex Hamiltonian systems
Santiago Barbieri, Luca Biasco, Luigi Chierchia +1
In this note, we briefly discuss how singular KAM Theory - which was worked out in a previous work by L.B. and L.C. for the mechanical case - can b…
math.DS2024
Nearly-optimal effective stability estimates around Diophantine tori of Hölder Hamiltonians
Santiago Barbieri, Gerard Farré
We prove that the solutions of Hölder-differentiable Hamiltonian systems, associated to initial conditions in a small ball of radius around a Lagrangian, Diophantine,…
math.AG2024
Semi-algebraic Geometry and generic Hamiltonian stability
Santiago Barbieri
The steepness property is a local geometric transversality condition on the gradient of a -function which is fundamental in order to ensure the stability of sufficiently-regul…