Disk galaxies and dynamical systems with nonnegative curvature (Q1091836)

The disk stellar systems considered as dynamical systems with nonnegative two-dimensional curvature are investigated. It is shown that almost all these systems have regions of stochastic and regular (ordered) motions of positive measure (regular-stochastic or RS-systems). In stochastic regions consisting of several ergodic components with positive Krylov-Kolmogorov-Sinai (KS) entropy, these systems have no transversal fibers and are not Anosov U-systems. For Hénon-Heiles systems, the existence of strongly stable solutions is proved. This fact explains the appearance of the islands of stability on the Poincaré sections obtained by numerical methods. The obtained results indicate the crucial role of chaos and order in the dynamics of spiral galaxies and the ratio of measures of the regions with stochastic and ordered motions seems to be essential in the classification of these objects.