4 problems

Nussbaum's conjecture. The minimal period of $x$ is at most

Let $f\colon\operatorname{int}(\mathbb{R}^n_+)\to\operatorname{int}(\mathbb{R}^n_+)$ be nonexpansive with respect to Thompson's part metric, and let $\tau_n$ denote the optimal uni…

Cosmic convergence conjecture. The normalized orbit $\frac{T^{n}x}{\left\Vert T^{n}x\right\Vert }$ converges as $n\rightarrow\infty$.

Let $C$ be a bounded convex domain in $\mathbb{R\mathrm{^{N}}}$ equipped with Hilbert's metric $d$, and let $f:C\rightarrow C$ be a 1-Lipschitz map. Nussbaum–Vandehey conjecture. E…