论文标题
共性符号系统中的非扭曲托里
Non-twist tori in conformally symplectic systems
论文作者
论文摘要
圆环上的耗散机械系统具有与速度成比例的摩擦的摩擦，由环上的合成形式形成式图像建模，它们是将符号形式传输到本身的倍数（相结合因子小于1）的地图。了解吸引子上的结构和动态很重要。借助参数并在适当的非分类条件下，可以通过调整参数来获得它，它是一个吸引子，它是一个不变的圆环，其内部动力学与旋转相结合[CCDLL13]。通过与符号动力学的类比，在建立适当的扭曲和非扭曲不变的托里（或系统）的定义方面存在一些争论。本文的目的是两个方面：（a）在共性符合系统的家庭中建立适当的扭曲和非扭转不变托里的定义； （b）得出非扭转不变托里的计算算法。本文的最后一部分致力于实现算法，说明了本文中提出的定义，并探讨了非扭转托里的分解机制。为了简单起见，我们在此处考虑了2D系统，即在2D环中定义，但是对更高维度的概括很简单。
Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that transport the symplectic form into a multiple of itself (with a conformal factor smaller than 1). It is important to understand the structure and the dynamics on the attractors. With the aid of parameters, and under suitable non-degeneracy conditions, one can obtain that, by adjusting parameters, there is an attractor that is an invariant torus whose internal dynamics is conjugate to a rotation [CCdlL13]. By analogy with symplectic dynamics, there have been some debate in establishing appropriate definitions for twist and non-twist invariant tori (or systems). The purpose of this paper is two-fold: (a) to establish proper definitions of twist and non-twist invariant tori in families of conformally symplectic systems; (b) to derive algorithms of computation of non-twist invariant tori. The last part of the paper is devoted to implementations of the algorithms, illustrating the definitions presented in this paper, and exploring the mechanisms of breakdown of non-twist tori. For the sake of simplicity we have considered here 2D systems, i.e. defined in the 2D annulus, but generalization to higher dimensions is straightforward.
