5 problems

Let $\gamma_0$ be an initial curve in the horizontal unitrack construction, and let $\gamma_n$ denote the successive curves for $n\in\mathbb{N}$. The unitrack is the union of these…

Let $\gamma_0$ be an initial curve in the horizontal unitrack construction, and let $\gamma_n$ denote the successive curves. Call $\gamma_0$ trivial when it is the trivial initial…

Vertical amplitude conjecture. The sequence $V(\gamma_n)$ is unbounded. The preceding theorem establishes analogous linear bounds and unboundedness for the horizontal amplitudes…

Let $\Gamma$ be a simple strictly convex curve with hyperbolic or parabolic monodromy, and let $\gamma$ be the corresponding rear track with rotation number $\rho(\gamma)$. Positiv…

Let $F$ be a front-wheel path whose trajectory is a simple closed curve bounding a region of area $A$. For a bicycle of length $\ell$, let … be the bicycle monodromy, which maps an…