### Abstract

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 of prime periodic orbits with period . The error term is bounded, at least, by for arbitrarily small ϵ>0, where and are, respectively, the topological entropy and the maximal Lyapunov exponent of the semiflow.

Original language | English |
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Pages (from-to) | 1954-2000 |

Number of pages | 47 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 38 |

Issue number | 5 |

DOIs | |

Publication status | Published - Aug 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

**The error term in the prime orbit theorem for expanding semiflows.** / Tsujii, Masato.

Research output: Contribution to journal › Article

*Ergodic Theory and Dynamical Systems*, vol. 38, no. 5, pp. 1954-2000. https://doi.org/10.1017/etds.2016.113

}

TY - JOUR

T1 - The error term in the prime orbit theorem for expanding semiflows

AU - Tsujii, Masato

PY - 2018/8/1

Y1 - 2018/8/1

N2 - 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 of prime periodic orbits with period . The error term is bounded, at least, by for arbitrarily small ϵ>0, where and are, respectively, the topological entropy and the maximal Lyapunov exponent of the semiflow.

AB - 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 of prime periodic orbits with period . The error term is bounded, at least, by for arbitrarily small ϵ>0, where and are, respectively, the topological entropy and the maximal Lyapunov exponent of the semiflow.

UR - http://www.scopus.com/inward/record.url?scp=85010877225&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010877225&partnerID=8YFLogxK

U2 - 10.1017/etds.2016.113

DO - 10.1017/etds.2016.113

M3 - Article

AN - SCOPUS:85010877225

VL - 38

SP - 1954

EP - 2000

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 5

ER -