Index of a curve C:
$I_{C}$ is defined as the net number of counterclock wise revolutions made by the vector field as the vector field x moves once counterclockwise around the curve C.
If C is a simple closed curve enclosing an isolated fixed point $x^{\ast}$ the index is independent of the curve C as mentioned by Strogaz. I fail to see this. Can someone give me some insights?
Thanks in advance.