Boundedness of the Domain of Definition is Undecidable for Polynomial ODEs
Daniel Silva Graça, Jorge Buescu, Manuel L. Campagnolo · Electronic Notes in Theoretical Computer Science · 2008
Consider the initial-value problem with computable parameters { d x d t = p ( t , x ) x ( t 0 ) = x 0 , where p : R n + 1 → R n is a vector of polynomials and ( t 0 , x 0 ) ∈ R n + 1 . We show that the problem of determining whether the maximal interval of definition of this initial-value problem is bounded or not is in general undecidable.