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. It is well-known that, with the aid of parameters, and under suitable non-degeneracy conditions, one can obtain that there is an attractor that is an invariant torus whose internal dynamics is conjugate to a rotation. By analogy with symplectic dynamics, a natural question is establishing appropriate definitions for twist and non-twist invariant tori in conformally symplectic systems.

The main goals of this paper are: (a) to establish proper definitions of twist and non-twist invariant tori in families of conformally symplectic systems; (b) to interpret these definitions in terms of dynamical properties; (c) to derive algorithms to compute twist and non-twist invariant tori; (d) to implement these algorithms in examples; (e) to explore the mechanisms of breakdown of twist and non-twist invariant tori. Hence, the last part of the paper is devoted to implementations of the algorithms, illustrating the definitions presented in this paper, and studying robustness properties of invariant tori.

圆环上的耗散机械系统具有与速度成比例的摩擦力，它是通过环上的保形辛映射图建模的，该保形辛映射将辛形式传输到其自身的倍数中（保形因子小于1）。重要的是要了解吸引子的结构和动力学。众所周知，借助于参数并且在合适的非简并条件下，可以获得一个吸引子，该吸引子是不变的环面，其内部动力学与旋转共轭。通过与辛动力的类比，一个自然的问题是为保形辛系统中的扭曲和非扭曲不变托里建立适当的定义。

本文的主要目标是：（a）建立适形辛系统族中扭曲和非扭曲不变的托里的正确定义；（b）用动力学特性解释这些定义；（c）推导计算扭曲和非扭曲不变花托的算法；（d）在示例中实现这些算法；（e）探索扭曲和非扭曲不变花托的分解机理。因此，本文的最后一部分致力于算法的实现，说明本文提出的定义，并研究不变花托的鲁棒性。