Yao Tong

A prime orbit theorem for smooth surface diffeomorphisms

We establish a sharp prime orbit theorem for every homoclinic class of a $C^\infty$ diffeomorphism on a closed surface with positive topological entropy. Let $\mathcal{H}$ be a homoclinic class with topological entropy $h>0$. Then there exists a constant $\chi_2<0$ such that for any $\chi_1 \in (0, h)$, \[ \lim_{\subst...