Ordinary Differential Equations

Abstract

Let f be a C ¹ vector field on an open set U in E . If f(x _o ) = 0 for some x _o ∈U, if a: J →U is an integral curve for f, and there exists some t_o ∈J such that α(t _o ) = x _o , show that α(t) = x _o for all t∈J. (A point x _o such that f(x ₀ )= 0 is called a critical point of the vector field.)