Over-rotation intervals of bimodal interval maps

Abstract

We describe all bimodal over-twist patterns and 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 onto them the above results.

Keywords:

• Over-rotation pair
• over-rotation number
• pattern
• periodic orbit

AMS Classifications:

• Primary 37E05
• 37E15
• Secondary 37E45

Disclosure statement

No potential conflict of interest was reported by the authors.