5 problems

Let $\mathcal{V}=(\nu_1,\ldots,\nu_N)$ be the natural-frequency vector, let $\mathcal{D}(\mathcal{V})$ denote its frequency-diameter quantity, and let $\kappa_c(\mathcal{V})$ be th…

Let $\nu$ be a probability measure on $\mathbb{R}^3$, let $\bar{\nu}$ be its $(0,1)$-marginal, and let $\pi$ and $\bar{\pi}$ denote the invariant measure of the Markov local-field…

Let $d4a2,d4a2$ be path-complete Lyapunov functions in $d52f\mathrm{pc}(\Sigma)$ satisfying Assumption. Suppose that $d53d$ is a subset of linear invertible maps. The composition-l…

Let $G$ be the synchronisation diffeomorphism of the torus considered in the paper, and let $S$ and $R$ be the open basins of attraction of its corresponding asymptotically stable…

Weak-Lyapunov-functional conjecture. Either there is a constant $c\ge\frac12$ such that, whenever $\kappa>c\mathcal{D}(\mathcal{V})$, both models admit weak Lyapunov functionals, o…