Periodic points of Ruelle-expanding maps

TL;DR

This paper proves that for Ruelle-expanding maps, the zeta function is rational and the topological entropy equals the exponential growth rate of periodic points, providing key insights into their dynamical complexity.

Contribution

It establishes the rationality of the zeta function and the relationship between entropy and periodic points for Ruelle-expanding maps.

Findings

Zeta function is rational for Ruelle-expanding maps

Topological entropy equals exponential growth rate of periodic points

Provides a link between dynamical complexity and periodic orbits

Abstract

We prove that, for a Ruelle-expanding map, the zeta function is rational and the topological entropy is equal to the exponential growth rate of the periodic points.