Computability in planar dynamical systems

Graça, Daniel; Zhong, Ning

http://hdl.handle.net/10400.1/1005

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Authors

Graça, Daniel

Zhong, Ning

Abstract(s)

In this paper we explore the problem of computing attractors and their respective basins of attraction for continuous-time planar dynamical systems. We consider C1 systems and show that stability is in general necessary (but may not be sufficient) to attain computability. In particular, we show that (a) the problem of determining the number of attractors in a given compact set is in general undecidable, even for analytic systems and (b) the attractors are semi-computable for stable systems. We also show that the basins of attraction are semi-computable if and only if the system is stable.