Bicycle tracks with hyperbolic monodromy -- results and conjectures
Differential Geometry
2025-01-07 v2 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.2412.18676,
title = {Bicycle tracks with hyperbolic monodromy -- results and conjectures},
author = {G. Bor and L. Hernández-Lamoneda and S. Tabachnikov},
journal= {arXiv preprint arXiv:2412.18676},
year = {2025}
}