Pré-Publication, Document De Travail Année : 2024

Hyperbolic absolutely continuous invariant measures for C^r one-dimensional maps

Résumé

For r > 1, we show, using the Ledrappier-Young entropy characterization of SRB measures for non-invertible maps, that if a C^r map f of the interval or the circle has its Lyapunov exponent greater than 1/r log ||f ′ || ∞ on a set E of positive Lebesgue measure, then it admits hyperbolic ergodic invariant measures that are absolutely continuous with respect to the Lebesgue measure. We also show that the basins of these measures cover E Lebesgue-almost everywhere.

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Dates et versions

hal-04757392 , version 1 (29-10-2024)

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  • HAL Id : hal-04757392 , version 1

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Alexandre Delplanque. Hyperbolic absolutely continuous invariant measures for C^r one-dimensional maps. 2024. ⟨hal-04757392⟩
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