# 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 $$\begin{eqnarray}\exp \biggl(\biggl(1-\frac{1}{4\lceil \unicode[STIX]{x1D712}_{\text{max}}/h_{\text{top}}\rceil }+\unicode[STIX]{x1D700}\biggr)h_{\text… 6 Citations • Mathematics Communications in Mathematical Physics • 2017 We consider a R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} • Mathematics • 2015 We consider a$${\mathbb{R}}R-extension of one dimensional uniformly expanding open dynamical systems and prove a new explicit estimate for the asymptotic spectral gap. To get these results, we use
Transfer operators associated with a dynamical system T and a weight g are important tools to understand the statistical properties of T , under appropriate smoothness and hyperbolicity conditions.
This chapter presents a variant of Ruelle’s bound on the essential spectral radius of transfer operators associated with differentiable expanding dynamics and weights, replacing the Holder spaces by
The main result of this chapter is a variant of Ruelle’s theorem on the dynamical determinants of transfer operators associated with differentiable expanding dynamics and weights. The proof uses the
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