PermalinkSubmitted by rpotrie on Thu, 06/29/2017 - 11:59
Something is known about minimality of strong foliations for partially hyperbolic diffeomorphisms (see Bonatti-Diaz-Ures, Journal of the IMJ, 1 (2002) 513-541).
However, minimality of the strong unstable foliation even for Anosov of T^3 with 3-bundles (2-dimensional unstable) is open.
Unique ergodicity should (?) be understood with respect to 'transverse' invariant measures. They always exist because unstable leafs have polynomial growth of volume.
PermalinkSubmitted by shub on Mon, 07/10/2017 - 09:59
Once again, I think that unique ergodicity of the unstable foliation for a volume preserving partially hyperbolic diffeomorphism may be related to the the stable ergodicity of the diffeomorphism. But this is quite speculative.
Tags
Comments
Something is known about
Something is known about minimality of strong foliations for partially hyperbolic diffeomorphisms (see Bonatti-Diaz-Ures, Journal of the IMJ, 1 (2002) 513-541).
However, minimality of the strong unstable foliation even for Anosov of T^3 with 3-bundles (2-dimensional unstable) is open.
Unique ergodicity should (?) be understood with respect to 'transverse' invariant measures. They always exist because unstable leafs have polynomial growth of volume.
Once again, I think that
Once again, I think that unique ergodicity of the unstable foliation for a volume preserving partially hyperbolic diffeomorphism may be related to the the stable ergodicity of the diffeomorphism. But this is quite speculative.
Add a new comment