Power series expansions naturally arise whenever solutions of ordinary differential
equations are studied in the regime of perturbation theory. In the case of quasiperiodic …

John Mather's seminal works in Hamiltonian dynamics represent some of the most important
contributions to our understanding of the complex balance between stable and unstable …

These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and
Hamiltonian systems. They are based on a series of lectures given by the author at …

In the setting of the Weyl quantization on the flat torus T^n, we exhibit a class of wave
functions with uniquely associated Wigner probability measure, invariant under the …

In the framework of toroidal Pseudodifferential operators on the flat torus T^ n:=(R/2 π Z)^ n T
n:=(R/2 π Z) n we begin by proving the closure under composition for the class of Weyl …

This paper deals with the phase space analysis for a family of Schrödinger eigenfunctions ψ
ℏ on the flat torus 𝕋 n=(ℝ/2 π ℤ) n by the semiclassical Wave Front Set. We study those ψ ℏ …

In this article we discuss a weaker version of Liouville's Theorem on the integrability of
Hamiltonian systems. We show that in the case of Tonelli Hamiltonians the involution …

The aim of this paper is twofold. On the one hand, we discuss the notions of strong chain
recurrence and strong chain transitivity for flows on metric spaces, together with their …

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli
Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n …

For an integrable Hamiltonian systems with $ d $ degrees of freedom ($ d\geq 2$), we
consider quantitatively the existence and non-existence of the flow-invariant Lagrangian …