Entropy of holomorphic and rational maps: a survey
  We give a brief survey on the entropy of holomorphic self maps $f$ of compact K\"ahler manifolds, and rational dominating self maps   $f$ of smooth projective varieties. We emphasize the connection between the entropy and the spectral radii of the induced action of   $f$ on the homology of the compact manifold. The main conjecture for the rational maps states that modulo birational isomorphism all various notions of entropy and the spectral radii are equal. 
Shmuel Friedland