论文标题
每个差异性是接近身份图的总重归其化
Every diffeomorphism is a total renormalization of a close to identity map
论文作者
论文摘要
对于任何$ 1 \ le r \ le \ infty $，我们表明表格$ \ mathbb {r}/\ mathbb {z} \ times m $的每种差异性是$ c^r $ close to Identity映射的全型。换句话说，对于$ \ mathbb {r}/\ mathbb {z} \ times m $的每一个差异性$ f $ f $ of $ \ mathbb {r}/\ mathbb {z} \ times m $，都存在一个地图$ g $，任意接近身份，使得$ g $的第一个返回映射$ g $ of $ g $ to n of tomain to $ f $ conjugate to $ f $ and the of thit ymater and ymath/z e; \ times m $。这使我们能够将多个属性的存在在动态系统中的身份附近，例如是平滑体积形式的Bernoulli。
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.
