A generic C1 map has no absolutely continuous invariant probability measure

Artur Avila; Jairo Bochi

doi:10.1088/0951-7715/19/11/011

A generic C¹ map has no absolutely continuous invariant probability measure

Artur Avila, Jairo Bochi

Mathematics

Research output: Contribution to journal › Review article › peer-review

17 Scopus citations

Abstract

Let M be a smooth compact manifold of any dimension. We consider the set of C¹ 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 C¹ topology.

Original language	English (US)
Article number	011
Journal	Nonlinearity
Volume	19
Issue number	11
DOIs	https://doi.org/10.1088/0951-7715/19/11/011
State	Published - Nov 1 2006

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/0951-7715/19/11/011

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title = "A generic C1 map has no absolutely continuous invariant probability measure",

abstract = "Let M be a smooth compact manifold of any dimension. We consider the set of C1 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 C1 topology.",

author = "Artur Avila and Jairo Bochi",

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AU - Avila, Artur

AU - Bochi, Jairo

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N2 - Let M be a smooth compact manifold of any dimension. We consider the set of C1 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 C1 topology.

AB - Let M be a smooth compact manifold of any dimension. We consider the set of C1 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 C1 topology.

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DO - 10.1088/0951-7715/19/11/011

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VL - 19

JO - Nonlinearity

JF - Nonlinearity

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A generic C¹ map has no absolutely continuous invariant probability measure

Abstract

All Science Journal Classification (ASJC) codes

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