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- W2119731351 abstract "We consider an ergodic invariant measure µ for a smooth actionof Z k , k � 2, on a (k+1)-dimensional manifold or for a locally free smooth action of R k , k � 2 on a (2k + 1)-dimensional manifold. We prove that if µ is hyperbolic with the Lyapunov hyperplanes in general position and if one element in Z k has positive entropy, then µ 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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- W2119731351 date "2011-07-01" @default.
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- W2119731351 title "Nonuniform measure rigidity" @default.
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- W2119731351 doi "https://doi.org/10.4007/annals.2011.174.1.10" @default.
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