Monotonicity of the over-rotation intervals for bimodal maps

TL;DR

This paper proves that the over-rotation interval of bimodal interval maps varies monotonically with the map, establishing a connection between parameter sets and the interval's properties.

Contribution

It demonstrates the monotonicity of the over-rotation interval for bimodal maps, linking parameter connectedness to interval behavior.

Findings

Over-rotation interval is a monotone function of bimodal maps.

Connectedness of parameter sets corresponds to constant over-rotation intervals.

The result applies to the analysis of dynamical behavior in bimodal maps.

Abstract

We show that the connectedness of the set of parameters for which the over-rotation interval of a bimodal interval map is constant. In other words, the over-rotation interval is a monotone function of a bimodal interval map.