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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23021 |
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| _version_ | 1866910687663489024 |
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| author | Delplanque, Alexandre |
| author_facet | Delplanque, Alexandre |
| contents | 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 ' || $\infty$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperbolic absolutely continuous invariant measures for C^r one-dimensional maps Delplanque, Alexandre Dynamical Systems 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 ' || $\infty$ 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. |
| title | Hyperbolic absolutely continuous invariant measures for C^r one-dimensional maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2410.23021 |