Unique ergodicity conjecture for the Jeandel-Rao subshift

Let

be the Jeandel-Rao Wang shift. A dynamical system is **uniquely ergodic** when it has a unique shift-invariant probability measure; equivalently here, every valid configuration has a uniquely determined appearance frequency for each pattern. **Unique ergodicity conjecture for the Jeandel-Rao subshift.** The Jeandel-Rao subshift

is uniquely ergodic. The preceding discussion states this as an unresolved conjecture, concerning the pattern frequencies of configurations even though the shift is not minimal.

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Other statements of this same problem, merged from separate entries. Each is equivalent to the statement above — proving any one settles them all.

Unique ergodicity conjecture for the Jeandel–Rao subshift
Let $\Omega_0$ be the Jeandel–Rao Wang shift, which contains the proper minimal subshift $X_0$ . Unique ergodicity conjecture. The subshift $\Omega_0$ is uniquely ergodic. This would strengthen the known result that its proper minimal subshift $X_0$ is strictly ergodic, and concerns the ergodic behaviour of the full, non-minimal Jeandel–Rao shift.
source: Sébastien Labbé, “Rauzy induction of polygon partitions and toral Z^2-rotations”, arXiv:1906.01104 (2021).

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Primary source

Sébastien Labbé, Casey Mann and Jennifer McLoud-Mann, “Nonexpansive directions in the Jeandel-Rao Wang shift”, arXiv:2206.02414 (2023).

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Unique ergodicity conjecture for the Jeandel-Rao subshift

Unique ergodicity conjecture for the Jeandel–Rao subshift

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