© 2015 Elsevier Inc. The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the bifurcation diagram of the period function of X=-y∂x+((x+1)p-(x+1)q)∂y with q<p. This family was previously studied for q=1 by Y. Miyamoto and K. Yagasaki.
- Critical periodic orbit
- Period function