On free loop spaces of toric spaces
  Growth of the Hilbert-Poincar\"e series for the rational homology of the free loop space of a toric space is addressed. In case the toric space is a manifold, the structure of the fan dictates whether the Hilbert-Poincar\"e series has exponential growth. Applications are made to the existence of infinitely many geometrically distinct periodic geodesics. 
A. Bahri, M. Bendersky, S. Gitler, F. R. Cohen
math.AT