Time-Reversible Ergodic Maps and the 2015 Ian Snook Prize

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, $(q,p)\longleftrightarrow (q,-p)$ . Weak control of the temperature, $\propto p^2$ and its fluctuation, resulting in ergodicity, has recently been achieved in a three-dimensional 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 \ae sthetically interesting attractor-repellor pairs. We challenge the reader to find and explore such time-reversible dissipative maps. This challenge is the 2015 Snook-Prize Problem.