Eventually Expanding Maps

TL;DR

This paper proves that a specific class of piecewise linear maps with expanding and contracting branches become eventually piecewise expanding and exact, contributing to the understanding of their long-term dynamical behavior.

Contribution

It demonstrates that such maps are eventually piecewise expanding and exact, providing new insights into their dynamical properties.

Findings

The map is eventually piecewise expanding.

The map is exact.

The map exhibits long-term chaotic behavior.

Abstract

In this paper we show that the piecewise linear map f(x) = px for x in [0,1/p], and sx-s/p for x in (1/p,1], p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding and exact.