Hi, everyone. I am new here, so I hope I am follow the protocols. Please let me know otherwise. Also, I apologize for not knowing Latex yet, tho I hope to learn it soon. am trying to show that the vector field: X^2(del/delx)+del/dely Is not a complete vector field. I think this is from John Lee's book, but I am not sure (it was in my class notes.) From what I understand, we need to find the integral curves for the vector field first, i.e we need to solve the system: dx/dt=[x(t)]^2 and dy/dt=1 I found the solutions to be given by (1/(x+c),y+c') c,c' real constants. In my notes ( 2-yrs old, unfortunately) , there is a solution: Phi(x,t)=(1/(1-tx), y+t) somehow in function of (x,t) In addition, there is a statement that Phi(x,t) satisfies: Phi(x,t+s)=Phi(x,t)oPhi(x,t) (o = composition) and that Phi satisfies certain initial conditions (which were not given explicitly for the problem). I suspect this has to see with one-parameter groups, but I am not sure of it, and I don't understand them that well, nor the relation with complete V.Fields. I would appreciate any explanation or help.