Interval maps where every point is eventually fixed

TL;DR

This paper characterizes the forcing relation among orbit patterns in interval maps where every point eventually becomes fixed, providing a complete description of which patterns enforce others.

Contribution

It offers a comprehensive classification of forcing relations among orbit patterns in a specific class of interval maps, filling a gap in dynamical systems theory.

Findings

Complete description of forcing relations among orbit patterns

Identification of conditions for one pattern to force another

Clarification of the structure of eventually fixed trajectories

Abstract

Among the orbit patterns that force only eventually fixed trajectories, we completely describe the forcing relation, by answering the question: which orbit patterns force which others?