4 problems

A birational map is assumed to admit an algebraic entropy, measuring the asymptotic growth of the degrees of its iterates. Algebraic entropy conjecture. The condition that algebrai…

Full-rank Poisson-structure conjecture. The maps $P_{ii}$ and $D_{iii}$ either do not admit any full-rank Poisson structure, or, for every full-rank Poisson structure they admit, t…

Let $b_{1,j+1}$ be the coefficients defining a birational map … , and let $[x]_+=\max(x,0)$. Define … Let $\lambda_{\max}$ be the root of largest magnitude among the roots of these…

Let $F$ be the $k$-dimensional Lyness' map … with $a\geq 0$, acting on … A first integral is a function constant along the orbits of $F$, and the map is called integrable when it h…