Graph and backward asymptotics of the tent map

TL;DR

This paper extends the understanding of the dynamics of tent-like unimodal maps, focusing on their graph and backward asymptotics, generalizing previous results from S-unimodal maps.

Contribution

It generalizes existing results on graph and backward limits from S-unimodal maps to a broader class of tent-like unimodal maps.

Findings

Characterization of graph limits for tent-like unimodal maps

Analysis of backward asymptotic behavior in these maps

Extension of previous S-unimodal map results

Abstract

The tent map family is arguably the simplest 1-parametric family of maps with non-trivial dynamics and it is still an active subject of research. In recent works the second author, jointly with J. Yorke, studied the graph and backward limits of S-unimodal maps. In this article we generalize those results to tent-like unimodal maps. By tent-like here we mean maps that share fundamental properties that characterize tent maps, namely unimodal maps without wandering intervals nor attracting cycles and whose graph has a finite number of nodes.