Abstract:

This talk deals with non-autonomous periodic differential equations.
In dimension one we prove that the periods of the periodic solutions are divisors of $T$, the period of the equation. In the analytic setting we prove that for any finite set of divisors of $T$ it exists a differential equations with exactly these set of periods. In the smooth setting we prove the same result for any set of divisors of $T$. We also will see some examples in dimension two for which the period of the solutions does no keep any relation with the period of the equation.