6 problems

Algebraic-entropy criterion. The algebraic entropy of $$ should be positive if and only if

Eigenvalue read-off conjecture. If the deautonomisation is sufficiently general, then the value of the largest eigenvalue of the linear map on the Picard group, and hence the algeb…

Picard-action conjecture. For any confining mapping of the plane, the behaviour of the parameters satisfying the confinement constraints is governed by the linear action on the Pic…

Let $T_{\mathcal I,\mathcal J}$ be a universal pentagram map on $d$-tuples of twisted $n$-gons in ${\mathbb {RP}}^d$, determined by matrices $\mathcal I$ and $\mathcal J$. Let…

Let $T_*$ denote an integrable pentagram map on twisted $n$-gons in ${\mathbb {CP}}^d$, with parameters $n$, $m$, and $d$. A discrete map is included into a flow if it occurs as th…

Non-integrability conjecture. This generalized pentagram map is non-integrable. The conjecture is supported by computer experiments, alongside examples of both integrable and non-i…