COMPUTABILITY WITH LOW-DIMENSIONAL DYNAMICAL-SYSTEMS

It has been known for a short time that a class of recurrent neural ne tworks has universal computational abilities. These networks can be vi ewed as iterated piecewise-linear maps in a high-dimensional space. In this paper, we show that similar systems in dimension two are also ca pable of universal computations. On the contrary, it is necessary to r esort to more complex systems (e.g., iterated piecewise-monotone maps) in order to retain this capability in dimension one.