Complex statistics in Hamiltonian barred galaxy models
  We use probability density functions (pdfs) of sums of orbit coordinates,
over time intervals of the order of one Hubble time, to distinguish weakly from
strongly chaotic orbits in a barred galaxy model. We find that, in the weakly
chaotic case, quasi-stationary states arise, whose pdfs are well approximated
by $q$-Gaussian functions (with $1<q<3$), while strong chaos is identified by
pdfs which quickly tend to Gaussians ($q=1$). Typical examples of weakly
chaotic orbits are those that "stick" to islands of ordered motion. Their
presence in rotating galaxy models has been investigated thoroughly in recent
years due of their ability to support galaxy structures for relatively long
time scales. In this paper, we demonstrate, on specific orbits of 2 and 3
degree of freedom barred galaxy models, that the proposed statistical approach
can distinguish weakly from strongly chaotic motion accurately and efficiently,
especially in cases where Lyapunov exponents and other local dynamic indicators
appear to be inconclusive.
