The error term in the prime orbit theorem for expanding semiflows

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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 languageEnglish
Pages (from-to)1954-2000
Number of pages47
JournalErgodic Theory and Dynamical Systems
Volume38
Issue number5
DOIs
Publication statusPublished - Aug 1 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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