A noncircular oval with convex unit-tangent iterates

Dean Matthew Menezes

For an oriented regular plane curve $\gamma$, define $\mathcal{T}\gamma =\gamma +\tau$, where $\tau$ is its unit tangent. We construct a noncircular curve ${\Gamma }_0$ such that every iterate ${\mathcal{T}}^n{\Gamma }_0$, $n\g…