5 problems

A t.d.s. $(X,T)$ is a topological dynamical system, and positive entropy means that its topological entropy is positive. It has DC2 chaos when there is an uncountable set…

Conjecture on DC2 pairs for interval nads. For a nads on an interval, the limit map must have a DC2 pair.

Let $I=[0,1]$ and let $C(I,I)$ denote the space of continuous maps from $I$ to itself. Equip $C(I,I)\times C(I,I)$ with its usual product topology, and call a pair $(f,g)$ chaotic…

Distributional-chaos conjecture. If $T$ is chaotic in the sense of Devaney, then $T$ is distributionally chaotic.

Let $(I,f_{1,\infty})$ be a nonautonomous dynamical system with positive topological entropy, and suppose that $f_{1,\infty}$ converges pointwise to a map in $\mathcal C$. A pair o…