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- W2950678501 abstract "We consider an ergodic invariant measure $mu$ for a smooth action of $Z^k$, $k ge 2$, on a $(k+1)$-dimensional manifold or for a locally free smooth action of $R^k$, $k ge 2$ on a $(2k+1)$-dimensional manifold. We prove that if $mu$ is hyperbolic with the Lyapunov hyperplanes in general position and if one element of the action has positive entropy, then $mu$ is absolutely continuous. The main ingredient is absolute continuity of conditional measures on Lyapunov foliations which holds for a more general class of smooth actions of higher rank abelian groups." @default.
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- W2950678501 date "2008-03-20" @default.
- W2950678501 modified "2023-09-27" @default.
- W2950678501 title "Nonuniform measure rigidity" @default.
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