  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.
