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

Complex statistics in Hamiltonian barred galaxy models