Relative chaos in gravitating systems with massive centre
Abstract A geometric method, namely the Ricci curvature criterion, is used to study the relative instability of evolving N-body gravitating systems with massive centres. The performed numerical experiments show that the Ricci curvature decreases with the increase in central concentration, thus indicating an increasing instability for systems with massive centre — either in the form of a point mass or a core formed during the evolution of single and multimass systems. Simulations of such systems do indeed suggest that they have faster gravothermal evolution than less concentrated ones.
O. Introduction This lecture will unfortunately not be a systematic review of the subject of rigorous results in non-equilibrium statistical mechanics. A preliminary attempt to outline such a review led me quickly to the conclusion that the field is too diverse to be summarized in a single lecture. I have therefore decided instead to discuss a few related.works in depth. The works I have chosen are: 1. The paper of J. Fritz and R. L. Dobrushin[5] on two-dimensional dynamics. 2. The paper of W. Braun and K. Hepp[3] on classical mechanics in the Vlasov limit. 3. A recent preprint by H. van Beijeren, J. L. Lebowitz, H. Spohn, and myself[2] on autocorrelations and fluctuations in the dilute equilibrium hard-sphere gas.