DYNAMICS OF STRONGLY DISSIPATIVE SYSTEMS

The attractors in two-dimensional (2D) phase space of the strongly dis sipative Henon map are reduced to those of an effectively 1D map. From the grammar for this effectively 1D map we can generate all of the un stable periodic orbits, which are exactly consistent with those from t he 2D map obtained directly both with a Newton procedure and the techn iques of Biham and Wenzel [Phys. Rev. Lett. 63, 819 (1989)]. This idea provides a method to give a very precise and not too cumbersome estim ate of the characteristic quantities of strange attractors of strongly dissipative systems. It is also helpful to understand many observatio ns on high-dimensional systems both experimentally and numerically.