Every diffeomorphism is a total renormalization of a close to identity map
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910725871501312 |
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| author | Berger, Pierre Gourmelon, Nicolaz Helfter, Mathieu |
| author_facet | Berger, Pierre Gourmelon, Nicolaz Helfter, Mathieu |
| contents | For any $1\le r\le \infty$, we show that every diffeomorphism of a manifold of the form $\mathbb{R}/\mathbb{Z} \times M$ is a total renormalization of a $C^r$-close to identity map. In other words, for every diffeomorphism $f$ of $\mathbb{R}/\mathbb{Z} \times M$, there exists a map $g$ arbitrarily close to identity such that the first return map of $g$ to a domain is conjugate to $f$ and moreover the orbit of this domain is equal to $\mathbb{R}/\mathbb{Z} \times M$. This enables us to localize nearby the identity the existence of many properties in dynamical systems, such as being Bernoulli for a smooth volume form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09064 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Every diffeomorphism is a total renormalization of a close to identity map Berger, Pierre Gourmelon, Nicolaz Helfter, Mathieu Dynamical Systems For any $1\le r\le \infty$, we show that every diffeomorphism of a manifold of the form $\mathbb{R}/\mathbb{Z} \times M$ is a total renormalization of a $C^r$-close to identity map. In other words, for every diffeomorphism $f$ of $\mathbb{R}/\mathbb{Z} \times M$, there exists a map $g$ arbitrarily close to identity such that the first return map of $g$ to a domain is conjugate to $f$ and moreover the orbit of this domain is equal to $\mathbb{R}/\mathbb{Z} \times M$. This enables us to localize nearby the identity the existence of many properties in dynamical systems, such as being Bernoulli for a smooth volume form. |
| title | Every diffeomorphism is a total renormalization of a close to identity map |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2210.09064 |