Abstract
We describe a method for carrying out a computation of the entropy function of the invariant set of a particular class of maps. We illustrate the method for the case of the quadratic and the Feigenbaum map. Elementary consequences of the symbolic dynamics associated with a map f lead to an algorithm that is a novel application of the Monte Carlo method. To sample, we use the fact that the salient features of the thermodynamic properties of the map are captured by its symbolic dynamics. In the symbolic domain, samples are chosen by manipulating character strings, rather than by performing floating-point calculations. Therefore, exact symbolic answers can be obtained by purely combinatorial methods. These symbolic answers then provide a recipe for performing high-precision numerical computations.
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