Time-reversible dissipative ergodic maps

We construct especially simple families of piecewise-linear two-dimensional continuous maps. These maps generate sets of points resembling continuous dynamical trajectories sampled at discrete times. The generated sets of points share many properties with nonequilibrium many-body phase-space trajectories. These characteristic properties include (i) time reversibility, (ii) multifractal attractor-repellor pairs, and (iii) ergodicity, without stable fixed points or holes.