7 problems

Let a bicycle segment have unit length, and let its front track be a closed convex curve bounding an area greater than $\pi$. The associated monodromy is the Möbius transformation…

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 $\Gamma$ be a closed strictly convex curve, let $\ell$ be the bicycle length, and consider the type of its bicycling monodromy as $\ell$ varies. Monodromy transition conjecture…

Let $\Gamma$ be a smooth strictly convex front track whose bicycling monodromy is hyperbolic or parabolic, and let $\gamma$ be a corresponding closed rear track. Its integer-valued…