The positive-entropy stable ergodicity conjecture

At least 6 years old · documented by

Let MM be a compact manifold, let mm denote Lebesgue measure, and let Diff⁡m1(M)\operatorname{Diff}^{1}_{m}(M) be the space of C1C^1 Lebesgue-measure-preserving diffeomorphisms. A diffeomorphism is stably ergodic if every sufficiently close diffeomorphism in the relevant volume-preserving C1C^1 neighborhood is ergodic. Positive-entropy stable ergodicity conjecture. Generically in Diff⁡m1(M)\operatorname{Diff}^{1}_{m}(M), if ff has positive metric entropy with respect to Lebesgue measure, then ff is stably ergodic. The conjecture was originally posed in dimension 33 and is stated here in arbitrary dimension. It was reported as proved in any dimension, so its status is solved.

References

Primary source

Gabriel Nuñez and Jana Rodriguez Hertz, “Stable minimality of expanding foliations”, arXiv:1908.09079 (2020).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.