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
