MAP WITH MORE THAN 100 COEXISTING LOW-PERIOD PERIODIC ATTRACTORS

We study the qualitative behavior of a single mechanical rotor with a small amount of damping. This system may possess an arbitrarily large number of coexisting periodic attractors if the damping is small enoug h. The large number of stable orbits yields a complex structure of clo sely interwoven basins of attraction, whose boundaries fill almost the whole state space. Most of the attractors observed have low periods, because high period stable orbits generally have basins too small to b e detected. We expect the complexity described here to be even more pr onounced for higher-dimensional systems, like the double rotor, for wh ich we find more than 1000 coexisting low-period periodic attractors.