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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.13524 |
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| _version_ | 1866909109966602240 |
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| author | de Faria, Edson Guarino, Pablo Nussenzveig, Bruno |
| author_facet | de Faria, Edson Guarino, Pablo Nussenzveig, Bruno |
| contents | Let $f$ be a $C^{1+bv}$ circle diffeomorphism with irrational rotation number. As established by Douady and Yoccoz in the eighties, for any given $s>0$ there exists a unique automorphic measure of exponent $s$ for $f$. In the present paper we prove that the same holds for multicritical circle maps, and we provide two applications of this result. The first one, is to prove that the space of invariant distributions of order 1 of any given multicritical circle map is one-dimensional, spanned by the unique invariant measure. The second one, is an improvement over the Denjoy-Koksma inequality for multicritical circle maps and absolutely continuous observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13524 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Automorphic measures and invariant distributions for circle dynamics de Faria, Edson Guarino, Pablo Nussenzveig, Bruno Dynamical Systems Primary 37E10, Secondary 37C40 Let $f$ be a $C^{1+bv}$ circle diffeomorphism with irrational rotation number. As established by Douady and Yoccoz in the eighties, for any given $s>0$ there exists a unique automorphic measure of exponent $s$ for $f$. In the present paper we prove that the same holds for multicritical circle maps, and we provide two applications of this result. The first one, is to prove that the space of invariant distributions of order 1 of any given multicritical circle map is one-dimensional, spanned by the unique invariant measure. The second one, is an improvement over the Denjoy-Koksma inequality for multicritical circle maps and absolutely continuous observables. |
| title | Automorphic measures and invariant distributions for circle dynamics |
| topic | Dynamical Systems Primary 37E10, Secondary 37C40 |
| url | https://arxiv.org/abs/2306.13524 |