3 problems

Let $\mathcal{R}$ be the collection of all maps $\mathcal{F}:[0,1]\to[0,1]$ that serve as factor maps for first-return maps $\psi_v:R\setminus W\to R$ of the Lorenz attractor, not…

Let $F=F_\theta$ be the map of the square ${\mathcal S}$, with parameter $\theta\in(0,\frac{\pi}{4})$. An ergodic decomposition conjecture asserts that, for Lebesgue almost all…

Let $\lambda$ be a real number with $|\lambda|<2$. Consider an integer sequence $(a_k)_{k\in\mathbb Z}$ satisfying … for every $k\in\mathbb Z$. Periodicity conjecture. Every such s…