caa a22 4500 46789146X CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-006-9095-x doi (NATIONALLICENCE)springer-10.1007/s10955-006-9095-x Gravitational Collapse and Ergodicity in Confined Gravitational Systems [Elektronische Daten] [Lj. Milanović, H. Posch, W. Thirring] The ergodic properties of many-body systems with repulsive-core interactions are the basis of classical statistical mechanics and are well established. This is not the case for systems of purely-attractive or gravitational particles. Here we consider two examples, (i) a family of one-dimensional systems with attractive power-law interactions, $$|x_i -x_j|^{\nu} \;, \; \nu > 0$$ , and (ii) a system of N gravitating particles confined to a finite compact domain. For (i) we deduce from the numerically-computed Lyapunov spectra that chaos, measured by the maximum Lyapunov exponent or by the Kolmogorov-Sinai entropy, increases linearly for positive and negative deviations of ν from the case of a non-chaotic harmonic chain (ν = 2). For $$2 < \nu \le 3$$ there is numerical evidence for two additional hitherto unknown phase-space constraints. For the theoretical interpretation of model (ii) we assume ergodicity and show that for a small-enough system the reduction of the allowed phase space due to any other conserved quantity, in addition to the total energy, renders the system asymptotically stable. Without this additional dynamical constraint the particle collapse would continue forever. These predictions are supported by computer simulations. Springer Science+Business Media, Inc., 2006 Milanović Lj Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria aut Posch H. Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria aut Thirring W. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 843-858 0022-4715 124:2-4<843 2006 124 10955 https://doi.org/10.1007/s10955-006-9095-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9095-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Milanović Lj Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria aut NATIONALLICENCE 700 1- Posch H. Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria aut NATIONALLICENCE 700 1- Thirring W. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 843-858 0022-4715 124:2-4<843 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer