Over-rotation intervals of bimodal interval maps

TL;DR

This paper characterizes over-rotation intervals for bimodal interval maps, providing an algorithm to determine these intervals and extending results to a new class called well behaved maps.

Contribution

It introduces an algorithm for computing over-rotation interval endpoints and generalizes results to well behaved polymodal maps.

Findings

Complete description of bimodal over-twist patterns

Algorithm for determining over-rotation interval endpoints

Extension of results to well behaved polymodal maps

Abstract

We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal interval maps called well behaved, and generalize the above results onto well behaved maps.