We show that multifractal measures arising from the symbolic dynamics of chaotic systems can be reproduced using iterated-functions system involving Möbius maps. This powerful approximation scheme is exact for hyperbolic billiards: The coding measures of zero-angle N-sided polygonal billiards are exactly rendered by N-1 Möbius maps. We also approximate with success the coding measures for the anisotropic Kepler system.

• Received 26 October 1990

DOI:https://doi.org/10.1103/PhysRevLett.66.2939