Santiago Barbieri

collaborators

4 papers

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 $ρ > 0$ around a Lagrangian, $(γ, τ) -$ 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 $C^{2}$ -function which is fundamental in order to ensure the stability of sufficiently-regul…

math.DS2022

Analytic Smoothing and Nekhoroshev estimates for Hölder steep Hamiltonians

Santiago Barbieri, Jean-Pierre Marco, Jessica Elisa Massetti

In this paper we prove the first result of Nekhoroshev stability for steep Hamiltonians in Hölder class. Our new approach combines the classical theory of normal forms in analytic…

math.AG2022

Bernstein-Remez inequality for Nash functions: A complex analytic approach

Santiago Barbieri, Laurent Niederman

Consider an open, bounded set $Ω \subset C$ , a positive integer $k$ and a compact $K \subset Ω$ of cardinality strictly greater than $k$ . We prove that, for any fu…