In section 2.9 of the book “Notes on Dynamical Systems” by Moser and Zehnder, it is proved the following theorem as a corollary of the Poincaré-Birkhoff fixed point theorem:

Theorem: On a **strictly** convex billiard table, there exist infinitely many distinct periodic orbits.

Is the result, or a weaker version of it, still true for convex tables?

C’mon Alfonso, this one’s for you! 😉