To characterize transport in a deterministic dynamical system is to compute exit time
distributions from regions or transition time distributions between regions in phase space …

Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …

In this paper, we present and illustrate a general methodology to apply KAM theory in
particular problems, based on an a posteriori approach. We focus on the existence of real …

Rotational invariant circles of area-preserving maps are an important and well-studied
example of KAM tori. John Greene conjectured that the locally most robust rotational circles …

We consider perturbations of integrable, area preserving nontwist maps of the annulus
(those are maps in which the twist condition changes sign). These maps appear in a variety …

We formulate and justify rigorously a numerically efficient criterion for the computation of the
analyticity breakdown of quasi-periodic solutions in symplectic maps (any dimension) and …

We study sequences of periodic orbits and the associated phase space dynamics in a 4-D
symplectic map of interest to the problem of beam stability in circular particle accelerators …

We study the breakdown of rotational invariant tori in 2D and 4D standard maps by
implementing three different methods. First, we analyze the domains of analyticity of a torus …

Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving
maps. Codimension-one tori are particularly important as they form barriers to transport …

Graphene and other recently developed two-dimensional materials exhibit exceptionally
strong in-plane stiffness. Relaxation of few-layer structures, either freestanding or on slightly …