The error term in the prime orbit theorem for expanding semiflows
| Autor: | Masato Tsujii |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics 010102 general mathematics Topological entropy Lyapunov exponent Function (mathematics) 01 natural sciences Suspension (topology) Prime (order theory) symbols.namesake Bounded function 0103 physical sciences symbols Orbit (dynamics) Asymptotic formula 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Ergodic Theory and Dynamical Systems. 38:1954-2000 |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/etds.2016.113 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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