The saga of a fish: from a survival guide to closing lemmas
The saga of a fish: from a survival guide to closing lemmas
复制标题
鱼的传奇：从生存指南到结束引理
DOI：
10.1016/j.jde.2019.04.010
复制
发表时间：
2018
影响因子：
2.4
通讯作者：
E. Stepanov
中科院分区：
文献类型：
--
作者：
S. Kryzhevich;E. Stepanov
在D. Burago，S. Ivanov和A.诺维科夫，“弱鱼的生存指南”，它已经表明，一个有限速度的鱼可以达到任何点在（可能无界）海洋提供的流体速度场是不可压缩的，有界的，并有消失的平均漂移。这一结果推广了一些已知的全局能控性定理，但基本上是非构造性的。我们给一条鱼一个不同的食谱如何生存在一个动荡的海洋，并显示其关系的动力系统的结构稳定性，通过提供一个建设性的方式来稍微改变速度场产生保守的（在这个意义上没有流浪集的积极措施）动态。特别地，这导致了C的扩展。无界域上不可压缩向量场的Pugh闭引理。结果是基于推广的Poincaré递归定理的一些σ-有限措施和特别构造的牛顿势。
In the paper by D. Burago, S. Ivanov and A. Novikov, “A survival guide for feeble fish”, it has been shown that a fish with limited velocity can reach any point in the (possibly unbounded) ocean provided that the fluid velocity field is incompressible, bounded and has vanishing mean drift. This result extends some known global controllability theorems though being substantially nonconstructive. We give a fish a different recipe of how to survive in a turbulent ocean, and show its relationship to structural stability of dynamical systems by providing a constructive way to change slightly the velocity field to produce conservative (in the sense of not having wandering sets of positive measure) dynamics. In particular, this leads to the extension of C. Pugh's closing lemma to incompressible vector fields over unbounded domains. The results are based on an extension of the Poincaré recurrence theorem to someσ-finite measures and on specially constructed Newtonian potentials.
时间上的弱鱼——相关水域和 G 方程的均质化
影响因子：
3
作者：
Burago, Dmitri;Ivanov, Sergei;Novikov, Alexei
通讯作者：
Novikov, Alexei