Boundedness of the Domain of Definition is Undecidable for Polynomial ODEs

Consider the initial-value problem with computable parameters{dxdt=p(t,x)x(t0)=x0, where p:Rn+1→Rn is a vector of polynomials and (t0,x0)∈Rn+1(t0,x0)∈Rn+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.