8 problems

Boshernitzan–Kornfeld's conjecture. For every $r\geqslant 2$, the set of infinite-type interval translation maps on $r$ intervals has Lebesgue measure zero in the parameter space…

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…

Let $\mathrm{ITM}(r)$ be the full parameter space of interval translation maps with $r$ translation intervals, equipped with its parameter-space measure. An infinite-type map is on…

Let a stable region be a region of stable interval translation maps, and let an infinite-type map be an interval translation map that is not of finite type. Accumulation of infinit…

Let an interval translation map be eventually periodic when its critical points eventually become periodic, and let a stable region be a region of stable maps in the parameter spac…

Let a stable region be a connected region in the parameter space of interval translation maps on which the maps are stable, and let its boundary consist of the maps obtained at the…

Syndetic recurrence conjecture. Almost all points of $M(S)$ are syndetically recurrent.

Metric conjugacy conjecture. Every ITM endowed with $\mu^*$ is metrically conjugated to an IEM, possibly with more than $n$ intervals. The conjugacy is expected to be continuous al…