5 problems

Let $q$ be an odd prime power and let $n\geq 3$. A quadratic system is a map … where each $f_i\in\mathbb{F}_q[x_1,\dots,x_n]$ has degree at most $2$. Classification conjecture. Suc…

Let the quadratic family be the parameterized family of quadratic maps, and call an invariant probability measure an acip when it is absolutely continuous with respect to Lebesgue…

Let $A(m,n)$ and $B(m,n)$ be the integer forms parametrizing rational $3$-cycles of maps $f_c(x)=x^2+c$, and let $(m,n)\in\mathbb{Z}^2$ satisfy $mn(m+n)\neq0$ and $\gcd(m,n)=1$. Nu…

Let a minimal unimodal combinatorics be a minimal combinatorial type in the unimodal region, and call it unobstructed when it is realized by the corresponding quadratic dynamical s…

No-long-cycles conjecture. The map $\phi$ has no $\mathbb{Q}$-periodic point of period greater than or equal to $3$.