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… 

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