Is topological entropy computable?

Anca Radulescu
Applied Mathematics

The topological entropy of a map measures in some sense the complexity of the corresponding dynamical system, by counting how many "very different" orbits of arbitrarily large length we can find. The question is weather entropy can be computed (in theory, and, if possible, in practice) up to an error which can be made arbitrarily small.

One quite general computation method, based on exponential growth of length, was studied by Newhouse and Pignataro. For piecewise monotone interval mappings, probably the simplest interesting dynamical systems, there is an effective computation that depends on being able to order finitely many forward images of critical points. I will be offering a possible rival computation: an algorithm based on kneading theory, which may not have the same degree of generality, but which would give a better entropy estimate much faster when it applies.