论文标题
关于线程离散模型的非整合性和动力学
On the non-integrability and dynamics of discrete models of threads
论文作者
论文摘要
在本文中，我们研究了平面$ n $ gons的动态，可以将其视为离散的线程模型。本文的主要结果是，在某些薄弱的假设下，这些系统在liouville的意义上是不可集成的。这既适用于完全自由的线程，又适用于放置在外部力场中的固定点的螺纹。我们为此类系统中拓扑熵的积极性提供了足够的条件。我们简要考虑离散线程的其他动力学属性，还考虑了不可延迟但可压缩线程的离散模型。
In the paper, we study the dynamics of planar $n$-gons, which can be considered as discrete models of threads. The main result of the paper is that, under some weak assumptions, these systems are not integrable in the sense of Liouville. This holds for both completely free threads and for threads with fixed points that are placed in external force fields. We present sufficient conditions for the positivity of topological entropy in such systems. We briefly consider other dynamical properties of discrete threads and we also consider discrete models of inextensible yet compressible threads.
