Computation with real numbers and continuous-time dynamical systems

Graça, Daniel

http://hdl.handle.net/10400.1/27329

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Authors

Graça, Daniel

Abstract(s)

In this paper we review some results about the interconnections between computation with real numbers and continuous dynamical systems. In particular, we take two complementary approaches: (i) to use standard computational models or theories such as Turing machines or computable analysis to understand which properties of continuous dynamical systems can be computed and (ii) to use continuous dynamical systems directly as models of computation and study their computational power. We will be particularly interested in continuous dynamical systems defined with analytic ordinary differential equations and, in particular, in dynamical systems defined with polynomial ordinary differential equations.