Eventually Expanding Maps
Peyman Eslami, Pawel Gora

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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Mathematics and Applications
