This paper is a review of results which have been recently obtained by applying
mathematical concepts drawn, in particular, from differential geometry and topology, to the …

Dynamical systems and their linear stability; 2. Topological chaos; 3. Liouvillian dynamics; 4.
Probabalistic chaos; 5. Chaotic scattering; 6. Scattering theory of transport; 7. Hydrodynamic …

Phase transitions are among the most impressive phenomena occurring in nature. They are
an example of emergent behavior, ie, of collective properties having no direct counterpart in …

The Hamiltonian dynamics of the classical planar Heisenberg model is numerically
investigated in two and three dimensions. In three dimensions peculiar behaviors are found …

A nonvanishing Lyapunov exponent λ 1 provides the very definition of deterministic chaos in
the solutions of a dynamical system; however, no theoretical mean of predicting its value …

We briefly review some of the most relevant results that our group obtained in the past, while
investigating the dynamics of the Fermi–Pasta–Ulam (FPU) models. The first result is the …

We perform the study of the stability of the Lorenz system by using the Jacobi stability
analysis, or the Kosambi–Cartan–Chern (KCC) theory. The Lorenz model plays an important …

The dynamics of the three coupled bosonic wells (trimer) containing N bosons is
investigated within a standard (mean-field) semiclassical picture based on the coherent …

A general method to describe Hamiltonian chaos in the thermodynamic limit is presented
which is based on a model equation independent of the dynamics. This equation is derived …

The parametric instability contribution to the largest Lyapunov exponent λ 1 is derived for a
mean-field Hamiltonian model, with attractive long-range interactions. This uses a recent …