The Hormander index of symmetric periodic orbits
  A symmetric periodic orbit is a special kind of periodic orbit that can also be regarded as a Lagrangian intersection point. Therefore it has two Maslov indices whose difference is the Hormander index. In this paper we provide a formula for the Hormander index of a symmetric periodic orbit and its iterates in terms of Chebyshev polynomials. 
Urs Frauenfelder and Otto van Koert
math.SG