I'm reading an article and it states the following:
Then, the factor is an integrating factor of the system (referring to a certain differential equation system), hence the system is integrable and its first integral is smooth in $\mathbb{R^2}$. So it doesn't have limit cycles.
I don't understand this part. What theorem are they using to say from the first integral of a system that it has not limit cycles?
Thanks for your time.