Nonlinear dynamical and control systems are an important source of applications for theories of computation over the the real numbers, since these systems are usually to complicated to study analytically, but may be extremely sensitive to numerical error. Further, computerassisted proofs and verification problems require a rigorous treatment of numerical errors. In this paper we will describe how to provide a semantics for effective computations on sets and maps and show how these operations have been implemented in the tool Ariadne for the analysis, design and verification of nonlinear and hybrid systems.
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S.B. Cooper , B. Loewe , A. Sorbi
Lecture Notes in Computer Science
Computational Topology for Systems and Control
Computability in Europe
Scientific Computing

Collins, P.J. (2007). Effective computation for nonlinear systems. In S.B Cooper, B Loewe, & A Sorbi (Eds.), Proceedings of Conference on Computability in Europe 2010 (pp. 169–178). Springer.