• DOI:10.1017/etds.2016.113
• Corpus ID: 119310271

The error term in the prime orbit theorem for expanding semiflows

@article{Tsujii2015TheET,
  title={The error term in the prime orbit theorem for expanding semiflows},
  author={Masato Tsujii},
  journal={Ergodic Theory and Dynamical Systems},
  year={2015},
  volume={38},
  pages={1954 - 2000}
}

• M. Tsujii
• Published 2 February 2015
• Mathematics
• Ergodic Theory and Dynamical Systems

We consider suspension semiflows of angle-multiplying maps on the circle and study the distributions of periods of their periodic orbits. Under generic conditions on the roof function, we give an asymptotic formula on the number $\unicode[STIX]{x1D70B}(T)$ of prime periodic orbits with period $\leq T$ . The error term is bounded, at least, by $$\begin{eqnarray}\exp \biggl(\biggl(1-\frac{1}{4\lceil \unicode[STIX]{x1D712}_{\text{max}}/h_{\text{top}}\rceil }+\unicode[STIX]{x1D700}\biggr)h_{\text{top}}\cdot T\biggr)\quad \text{in the limit }T\rightarrow \infty\end{eqnarray}$$ for arbitrarily small $\unicode[STIX]{x1D700}>0$ , where $h_{\text{top}}$ and $\unicode[STIX]{x1D712}_{\text{max}}$ are, respectively, the topological entropy and the maximal Lyapunov exponent of the semiflow.