Properties of stellar trajectories in numerical dynamical models of open star clusters

Stellar trajectories in models of open star clusters that are nonstationary in the regular field of the cluster are analyzed. The maximum characteristic Lyapunov exponents λ of the trajectories of the stellar motions in the open cluster are estimated. The mean λ in the open-cluster models considered are \(\bar \lambda \simeq ({\rm M}yr)^{ - 1} \). Cluster cores and halos are regions of highly stochastic and more ordered stellar motions, respectively. The mean Lyapunov exponent, \(\bar \lambda \), increases with the cluster density, as does the size of the highly stochastic region in the cluster core. The stellar trajectories in phase space are “glued” to a domain with a given λ. A Fourier analysis of the stellar trajectories in the open-cluster models is performed. The distributions of the periods of the stellar trajectories with the highest power-spectrum levels are constructed. The distributions of the periods corresponding to the most significant oscillations of the stellar trajectories exhibit peaks with periods commensurable with (or close to) those of the most significant oscillations of the regular field of the system. Specific features of the distributions of the periods of the most significant oscillations of the stellar trajectories and the origins of the formation of these features in the open-cluster models are discussed.