On the Validity of the Conjugate Pairing Rule for Lyapunov Exponents
| dc.creator | Bonetto, F. | |
| dc.creator | Cohen, E. G. D. | |
| dc.creator | Pugh, C. | |
| dc.date | 1998-03-09 | |
| dc.date.accessioned | 2026-07-07T02:35:23Z | |
| dc.date.available | 2026-07-07T02:35:23Z | |
| dc.description | For Hamiltonian systems subject to an external potential, which in the presence of a thermostat will reach a nonequilibrium stationary state, Dettmann and Morriss proved a strong conjugate pairing rule (SCPR) for pairs of Lyapunov exponents in the case of isokinetic (IK) stationary states which have a given kinetic energy. This SCPR holds for all initial phases of the system, all times t and all numbers of particles N. This proof was generalized by Wojtkovski and Liverani to include hard interparticle potentials. A geometrical reformulation of those results is presented. The present paper proves numerically, using periodic orbits for the Lorentz gas, that SCPR cannot hold for isoenergetic (IE) stationary states, which have a given total internal energy. In that case strong evidence is obtained for CPR to hold for large N and t, where it can be conjectured that the larger N, the smaller t will be. This suffices for statistical mechanics. | |
| dc.description | 30 pages, 33 ps figure | |
| dc.identifier | https://arxiv.org/abs/chao-dyn/9803011 | |
| dc.identifier | http://arxiv.org/abs/chao-dyn/9803011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/15589 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | On the Validity of the Conjugate Pairing Rule for Lyapunov Exponents | |
| dc.type | text |