Mixing properties of a class of nonuniformly expanding maps. Application to H{ö}lderian invariance principles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916849455726592 |
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| author | Bigot, Aurélie Alouin, V |
| author_facet | Bigot, Aurélie Alouin, V |
| contents | We study the mixing properties of a class of nonuniformly expanding maps when the return time to the basis has a weak moment of order p >1, up to a slowly varying function. From these computations, we deduce an invariance principle in H{ö}lder spaces for the partial sum process of Birkhoff sums of H{ö}lder continuous observables. The results apply to a class of intermittent maps of the unit interval. For such a map, we also prove that the H{ö}lder invariance principle remains true for BV observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13529 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixing properties of a class of nonuniformly expanding maps. Application to H{ö}lderian invariance principles Bigot, Aurélie Alouin, V Dynamical Systems Probability We study the mixing properties of a class of nonuniformly expanding maps when the return time to the basis has a weak moment of order p >1, up to a slowly varying function. From these computations, we deduce an invariance principle in H{ö}lder spaces for the partial sum process of Birkhoff sums of H{ö}lder continuous observables. The results apply to a class of intermittent maps of the unit interval. For such a map, we also prove that the H{ö}lder invariance principle remains true for BV observables. |
| title | Mixing properties of a class of nonuniformly expanding maps. Application to H{ö}lderian invariance principles |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2502.13529 |