8 problems

Let $\frac{m}{p}\in\mathopen{}\mathclose\bgroup\originalleft(0,\frac{1}{2}\aftergroup\egroup\originalright)$ be a rotation number, and let $\frac{m^-}{p^-}$ and $\frac{m^+}{p^+}$ d…

Let the PLPDM family be the family of piecewise linear perturbations of the doubling map, and call post-critical combinatorics admissible when it satisfies the admissibility condit…

A piecewise linear dynamical system is assumed to arise from a prioritized Petri net, with the sufficient conditions and assumptions established in the paper ensuring the existence…

Let $\Phi^+(A_n)$ be the positive-root poset of type $A_n$, and let the rank-alternating order ideal cardinality statistic be … for an order ideal $I$ of $\Phi^+(A_n)$. Bernstein–S…

The type B piecewise-linear homomesy conjecture. The statistic $h^{\mathrm{PL}}_*\colon \mathcal{A}^{\mathrm{PL}}_{\kappa}(\mathsf{B}^n)\to \mathbb{R}$ is $\kappa$-mesic for…

Consider the general piecewise-linear map … with linear components $A_L$ and $A_R$ on the two sides of its switching manifold. A fixed point is asymptotically stable if it is Lyapu…

Let $P=[2]\times[2]$, let ${\mathcal O}(P)$ be its order polytope, and let $\phi_{\mathcal P}$ be the piecewise-linear map obtained by toggling the elements in the order $y,z,x,w$.…

Let $Y_m$ and $Z_m$ be solutions of ultradiscrete Painlevé VI without parity variables, with fixed parity variables $\frak{y}_m=\frak{z}_m=-1$ for all $m$, and let $Q,A_i,B_i$ be t…