Hi, everyone. I am new here, so I hope I am follow the protocols. Please(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# One- parameter groups

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