Boundedness of the domain of definition is undecidable for polynomial odes

Abstract

Consider the initial-value problem with computable parameters dx dt = p(t, x) x(t0) = x0, where p : Rn+1 ! Rn is a vector of polynomials and (t0, x0) 2 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.