4 problems

Let $f:[0,1]\to[0,1]$ be continuously differentiable, and let $s\alpha(x)$ denote a special $\alpha$-limit set. Differentiable-map conjecture. Every special $\alpha$-limit set of…

Let $f:[0,1]\to[0,1]$ be continuous, let $x\in[0,1]$, and let $s\alpha(x)$ be the special $\alpha$-limit set of $x$. Period-three coexistence conjecture. If $s\alpha(x)$ contains a…

Let $f:[0,1]\to[0,1]$ be continuous. A special $\alpha$-limit set $s\alpha(x)$ is the union of the accumulation-point sets of all backward orbit branches of $x$. Kolyada–Misiurewic…

Dissipativity conjecture. The product system $(I^2,f_2,\lambda_2)$ is dissipative.