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Computing domains of attraction for planar dynamics
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In this note we investigate the problem of computing the
domain of attraction of a
ow on R2 for a given attractor. We consider
an operator that takes two inputs, the description of the
ow and a cover
of the attractors, and outputs the domain of attraction for the given
attractor. We show that: (i) if we consider only (structurally) stable
systems, the operator is (strictly semi-)computable; (ii) if we allow all
systems de ned by C1-functions, the operator is not (semi-)computable.
We also address the problem of computing limit cycles on these systems.
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C. S. Calude, J. F. Costa, N. Dershowitz, E. Freire, and G. Rozenberg