Report
Every diffeomorphism is a total renormalization of a close to identity map
| العنوان: | Every diffeomorphism is a total renormalization of a close to identity map |
|---|---|
| المؤلفون: | Berger, Pierre, Gourmelon, Nicolaz, Helfter, Mathieu |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems |
| الوصف: | 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. Comment: To appear in Inventiones mathematicae. 29 pages, 8 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2210.09064 |
| رقم الانضمام: | edsarx.2210.09064 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |