Computable Analysis with Applications to Dynamic Systems

In this article we develop a theory of computation for continuous mathematics. The theory is based on earlier developments of computable analysis, especially that of the school of Weihrauch, and is presented as a model of intuitionistic type theory. Every effort has been made to keep the presentation as simple yet general as possible. The core subject matter of Turing computability and computable analysis should be accessible to non-specialists with a solid background in general topology and analysis, but important technical results are also proved. To show the potential use of the theory, some simple applications are given to dynamical systems and control theory.