An equivalent condition for Anosov maps with zero entropies

Sakai defined the Anosov maps on compact metric spaces. Sun proved that Anosovmaps have the orbit-topological stability, Markov partitions and ζ-funtions. Aformulation for the topological entropy of an Anosov map wes given by Sun in reference. In this note we will also study the topological entropy of an Anosov map, but we willpay attention to the relation between the entropy and the number of periodic points. Thefollowing consequenee will be proved.