Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak and strong chaos in FPU models and beyond   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. A first result is the numerical evidence of the existence of two
different kinds of transitions in the dynamics of the FPU models: i) a
Stochasticity Threshold (ST), characterized by a value of the energy per degree
of freedom below which the overwhelming majority of the phase space
trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as
the number N of degrees of freedom is increased. ii) a Strong Stochasticity
Threshold (SST), characterized by a value of the energy per degree of freedom
at which a crossover appears between two different power laws of the energy
dependence of the largest Lyapunov exponent, which phenomenologically
corresponds to the transition between weakly and strongly chaotic regimes. It
is stable with N. A second result is the development of a Riemannian geometric
theory to explain the origin of Hamiltonian chaos. The starting of this theory
has been motivated by the inadequacy of the approach based on homoclinic
intersections to explain the origin of chaos in systems of arbitrarily large N,
or arbitrarily far from quasi-integrability, or displaying a transition between
weak and strong chaos.
  Finally, a third result stems from the search for the transition between weak
and strong chaos in systems other than FPU.
  Actually, we found that a very sharp SST appears as the dynamical counterpart
of a thermodynamic phase transition, which in turn has led, in the light of the
Riemannian theory of chaos, to the development of a topological theory of phase
transitions.

36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc