8 problems

Conjecture on the necessity of global (PI). The gap between chamber-wise and global (PI) is structurally necessary in the non-injective setting; investigating this gap should lead…

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 $F$ be a group, let $G$ be the group under consideration, let $H$ be the relevant group, and let $A(G)$ denote the Fourier algebra of $G$. A mixed piecewise-affine map is a map…

Let $UT\subset\mathcal{E}$ be the set of untuned parameters, … Here a matching interval is non-neutral when its matching index is nonzero. Accumulation conjecture. Every element ……

Let $f$ be a piecewise-affine map of $\mathbb{Q}\hspace{0.5pt}^2$ and let $O$ be a bounded orbit of $f$. For each prime $p$, let $h$ and $h_p$ denote the global and $p$-adic height…

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…

Global attractivity conjecture. The origin is a globally attracting fixed point for this four-level asymmetric map. This would extend the class of asymmetric piecewise affine maps…

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…