11 problems

A Bruin–Troubetzkoy interval translation mapping (BT ITM) is the special class of interval translation mappings considered in the source, and an ITM is of infinite type when its at…

Let $d49c$ be the measure obtained in the theorem on unique ergodicity, and consider Bruin–Troubetzkoy interval translation maps of infinite type. Weak-mixing conjecture. Almost al…

Polygonal-billiard conjecture. For almost all simply connected polygonal tables, the billiard flow is ergodic and weakly mixing.

Directional weak-mixing conjecture. For every translation surface that does not factor over the circle, the directionally typical translation flow is weakly mixing.

Let $p(q)$ denote the word complexity of a subshift, namely the number of distinct words of length $q$, and suppose the subshift admits a weakly mixing probability measure. The qua…

Let $(X,\mathscr{B},\mu,T)$ be a measure-preserving system, let $U$ denote its Koopman operator, and let $f\in L^2(X,\mu)$ satisfy … for every $g\in L^2(X,\mu)$. A sequence…

Let $P$ be a polygonal table with a fixed number of vertices, and let its billiard flow be the flow obtained by elastic reflection at the sides of $P$. Gutkin–Katok conjecture. The…

Let $\pi:X\to Y$ be the factor map in the setting of the paper, and let $\pi^{-1}(y)$ denote the fiber over $y\in Y$. A subset of a dynamical system is $\Delta$-weakly mixing in th…

The weak-mixing invariant-scrambled-set conjecture. There exists a weakly mixing system with a fixed point but without invariant $\delta$-scrambled sets.

A KAM-type system is a dynamical system with regular and unstable regions of phase space; let an unstable region mean a region in which the motion is unstable. Weak-mixing conjectu…

Weak-mixing conjecture. For almost every $alpha":[0,1)$, the composition $T\circ R_{\alpha}$ is weak mixing.