Artur Avila, Jairo Bochi
Abstract
Let M be a smooth compact manifold of any dimension. We consider the set of C 1 maps f : M → M which have no absolutely continuous (with respect to Lebesgue) invariant probability measure. We show that this is a residual set in the C 1 topology.
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Let M be a smooth compact manifold of any dimension. We consider the set of C 1 maps f : M → M which have no absolutely continuous (with respect to Lebesgue) invariant probability measure. We show that this is a residual set in the C 1 topology.
Key concepts: Absolute continuity, Mathematics, Lebesgue measure, Probability measure, Invariant measure, Invariant (physics), Measure (data warehouse), Lebesgue integration