Ergodic Time-Reversible Chaos for Gibbs' Canonical Oscillator
William Graham Hoover
Ruby Valley Research Institute, Highway Contract 60, Box 601,
Ruby Valley, NV 89833, USA
Julien Clinton Sprott
Department of Physics, University of Wisconsin, Madison, WI
53706, USA
Puneet Kumar Patra
Advanced Technology Development Center, Department of Civil
Engineering, Indian Institute of Technology, Kharagpur, West
Bengal, 721302, India
Received 20 July 2015
Received in revised form 26 August 2015
Accepted 27 August 2015
Available online 1 September 2015
Communicated by C. R. Doering
ABSTRACT
Nose's pioneering 1984 work inspired a variety of
time-reversible deterministic thermostats. Though several groups
have developed successful
doubly-thermostated models,
single-thermostat models have failed to generate Gibbs'
canonical distribution for the one-dimensional harmonic
oscillator. A 2001 doubly-thermostated model, claimed to be
ergodic, has a singly-thermostated version. Though neither of
these models is ergodic this work has suggested a successful
route toward singly-thermostated ergodicity. We illustrate both
ergodicity and its lack for these models using phase-space cross
sections and Lyapunov instability as diagnostic tools.