A question on periodic orbits for billiards

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?

One thought on “A question on periodic orbits for billiards”

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.