14 problems

Let … be the semi-bounded parameter set, and for each real $\mu$ let … be the associated $l_{\infty}$-spectrum. Conjecture B. The set $\Omega_{SB}$ has positive two-dimensional Leb…

Suppose $\mathbf{g}$ is of type $A_n$, and let $\mathbf{i}$ be a reduced expression for the longest Weyl-group element $w_0$. Let $\mathbf{k}=(1,3,5,\ldots,2,4,6,\ldots)$ and…

Consider the class of two-dimensional piecewise linear discontinuous maps discussed in the paper, whose attractors include weird quasiperiodic attractors (WQAs). Under a parameter…

Let $T$colon $\mathbb{R}^n\to\mathbb{R}^n$ be an nD map as given in Definition 1, and let $\mathcal{A}$ be a bounded $\omega$-limit set different from the fixed point $O$ or from r…

Let $F$ be a discontinuous piecewise linear map possessing a weird quasiperiodic attractor (WQA), meaning an attractor with the intricate, potentially infinite-segment or seemingly…

Let $n\geq 1$ and let $\xi$ be a parameter in $\mathcal{R}^{(4)}_n$, where $\mathcal{R}^{(4)}_n$ is the region defined in the source by the corresponding inequalities involving…

Let $\xi$ be a parameter in $\mathcal{R}^{(4)}_0$, where $\mathcal{R}^{(4)}_0$ is the region defined by $\phi_{\rm min}(\xi)>0$, $\phi_{\rm min}(g(\xi))\leq 0$, and $\alpha(\xi)<0$…

Let $\xi$ be a parameter in the first region $\mathcal{R}^{(3)}_0$ of the non-invertible parameter region $\Phi^{(3)}$, where the BCNF is the map under study. Unique-attractor conj…

Let $\xi$ be a parameter in the region $\mathcal{R}^{(2)}_0$ of the orientation-reversing parameter space, and let $X$ denote the relevant fixed point of the map. Unique-attractor…

Let $J_1(xi)$ be the quantity used in the paper to establish the growth of line segments under iteration, and let $phi(g(xi))$ be the corresponding weaker criterion. Weaker-conditi…

The two-dimensional BCNF is a piecewise-linear map whose physically important parameter regime is denoted by $\mathcal{R}_{\rm BYG}$. Chaotic-attractor conjecture. A chaotic attrac…

Invariant compact-region conjecture. The existence of such a compact set $\Omega$ is equivalent to the asymptotic stability of $\b0$.

Let $F$ be a simply switched piecewise linear function, meaning that it has an abs-normal representation of switching depth $nu=1$. A map is open if it maps open sets to open sets,…

Let $F:\mathbb{R}^n\mapsto\mathbb{R}^m$ be a piecewise linear mapping. An abs-normal representation of $F$ has switching depth $u$, the least integer such that $L^nu=0$ for its st…