Diffeomorphism between an ellipse and unit circle? I'm trying to learn about diffeomorphism and an example asks for a diffeomorphism between an ellipse and an unit circle.
How does one construct such?

You need to use a specific ellipse, and presumably the person asking the question would not accept the unit circle as an example of an ellipse (in which case the identity mapping would deliver).
I would suggest using the standard equation of an ellipse with horizontal and vertical axes, centered on the origin. This is a scaled version of the unit circle with possibly different scaling factors in the horizontal and vertical directions. Scaling back provides an example of a diffeomorphism.
