Nonequilibrium potentials for dynamical systems with fractal attractors or repellers

The concept of a nonequilibrium potential is applied to dynamical systems with fractal attractors or repellers. In particular, we study the case of the Feigenbaum attractor in one-dimensional maps and the case of hyperbolic strange attractors or repellers in two-dimensional maps. The potential-height distribution of the latter is shown to exhibit multifractal features; that of the Feigenbaum attractor is characterized by a single number, the universal exponent for noisy period-doubling bifurcations.