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Time-Reversible Ergodic Maps and the 2015 Ian Snook Prizes

Hoover W. G., Hoover C. G.

Computational Methods in Science and Technology

2015

Vol. 21, No. 3

161--164

The time reversibility characteristic of Hamiltonian mechanics has long been extended to nonHamiltonian dynamical systems modeling nonequilibrium steady states with feedback-based thermostats and ergostats. Typical solutions are multifractal attractor-repellor phase-space pairs with reversed momenta and unchanged coordinates, (q; p)↔(q;--p). Weak control of the temperature, α p2 and its fluctuation, resulting in ergodicity, has recently been achieved in a threedimensional time-reversible model of a heat-conducting harmonic oscillator. Two-dimensional cross sections of such nonequilibrium flows can be generated with time-reversible dissipative maps yielding æsthetically interesting attractorrepellor pairs. We challenge the reader to find and explore such time-reversible dissipative maps. This challenge is the 2015 Snook-Prize Problem.