7 problems

Let $l\in\mathbb N$, and let the parameter $\mu$ satisfy one of the equations governing the relevant monodromy cases according as $l$ is odd or even. Consider the corresponding mon…

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…

Consider the Lyness map with parameter $\alpha>0$ and let $\rho^v_\alpha$ denote its rotation number as a function of the level parameter $v$. Zeeman's conjecture. The function…

Let $D$ be the domain under consideration, and let $\triangle P_1P_2P_3$ be a triangle in $D$. Write $\psi_{\triangle P_1P_2P_3}$ for its associated billiard map,…

Let $\lambda=a/b$ and $\delta=r/s$ be rational numbers with $0<\lambda,\delta<1$, and let $\gamma>1$. Theorem 2 concerns the rational rotation number $\rho_{\lambda,\delta}=p/q$ un…

Let $F$ be the free group generated by $a$ and $b$, and let $w\in [F,F]$. Commutator-subgroup rationality conjecture. Then … This is a rationality conjecture for the maximum of…

Let $w$ be a positive word of the form … Suppose that $R(w,r,s)=p/q$, where $p/q$ is reduced. Generalized lock inequality. Then … For the linear representation with $a=R_r$ and…