GEOMETRIC PROPERTIES OF PARTIALLY HYPERBOLIC MEASURES AND APPLICATIONS TO MEASURE RIGIDITY - Université Paris 8 Vincennes - Saint-Denis Access content directly
Preprints, Working Papers, ... Year : 2023

GEOMETRIC PROPERTIES OF PARTIALLY HYPERBOLIC MEASURES AND APPLICATIONS TO MEASURE RIGIDITY

Alex Eskin
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Rafael Potrie
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Abstract

We give a geometric characterization of the quantitative joint non-integrability, introduced by Katz in [Ka], of strong stable and unstable bundles of partially hyperbolic measures and sets in dimension 3. This is done via the use of higher order templates for the invariant bundles. Using the recent work of Katz, we derive some consequences, including the measure rigidity of uu-states and the existence of physical measures.
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Dates and versions

hal-04255429 , version 1 (24-10-2023)

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  • HAL Id : hal-04255429 , version 1

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Alex Eskin, Rafael Potrie, Zhiyuan Zhang. GEOMETRIC PROPERTIES OF PARTIALLY HYPERBOLIC MEASURES AND APPLICATIONS TO MEASURE RIGIDITY. 2023. ⟨hal-04255429⟩
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