In this paper we present an a-posteriori KAM theorem for the existence of an (n− d)-
parameter family of d-dimensional isotropic invariant tori with Diophantine frequency vector …

In this paper, we present evidence of the stability of a model of our Solar System when
taking into account the two biggest planets, a planar (Newtonian) Sun–Jupiter–Saturn …

We introduce a new class G sn of generic real analytic potentials on T n and study global
analytic properties of natural nearly–integrable Hamiltonians 1 2| y| 2+ ε f (x), with potential …

In this paper, we focus on distinguishing between the types of dynamical behavior that occur
for typical one-and two-dimensional torus maps, in particular without the assumption of …

The goal of this paper is to provide a methodology to prove existence of (fiberwise
hyperbolic) real-analytic invariant tori in real-analytic quasi-periodic skew-product dynamical …

This paper focuses on distinguishing classes of dynamical behavior for one-and two-
dimensional torus maps, in particular between orbits that are incommensurate, resonant …

We present an algorithm for the construction of lower dimensional elliptic tori in parametric
Hamiltonian systems by means of the parametrization method with the tangent and normal …

We present some computer assisted methods to prove the existence of spectral gaps for the
Almost Mathieu operator at critical coupling and give rigorous numerical estimates on their …

The goal of this paper is to provide a methodology to prove the existence of (fiberwise
hyperbolic) real-analytic invariant tori in real-analytic quasi-periodic skew-product dynamical …

This paper outlines an approach for proving existence of hyperbolic quasi-periodic invariant
tori using computer assisted methods based on an a posteriori KAM-like theorem. We …