Bicycle tracks with hyperbolic monodromy -- results and conjectures

TL;DR

This paper explores conditions for the bicycling monodromy of closed plane curves to be hyperbolic, introducing a hyperbolic development approach and proposing conjectures based on computational experiments.

Contribution

It provides new necessary and sufficient conditions for hyperbolic bicycling monodromy and introduces a hyperbolic development framework for analysis.

Findings

New criteria for hyperbolic monodromy in closed plane curves

Hyperbolic development as a key analytical tool

Conjectures on monodromy of convex curves based on experiments

Abstract

We find new necessary and sufficient conditions for the bicycling monodromy of a closed plane curve to be hyperbolic. Our main tool is the ``hyperbolic development" interpretation of the bicycling monodromy of plane curves. Based on computer experiments, we pose two conjectures concerning the bicycling monodromy of strictly convex closed plane curves.