It is proved that the topological entropy of a surface diffeomorphism is given by the growth rate of the number of periodic points of saddle type. It is also shown that the number of periodic points with weak hyperbolicity is small.
"Topological entropy and periodic orbits of saddle type for surface diffeomorphisms." Hiroshima Math. J. 33 (2) 189 - 195, July 2003. https://doi.org/10.32917/hmj/1150997945