We survey recent results on the theory of dynamical chaos from the point of view of topological dynamics. We present the concept of three types of dynamics: conservative, dissi-pative, and mixed dynamics, and also show several simple examples of attractors and repellers of all three types. Their similarities and differences with other known types of attractors and repellers (maximal and Milnor ones) are discussed. We also present elements of the qualitative theory of mixed dynamics of reversible systems. As examples of such systems we consider three nonholonomic models of rigid body motion: the Suslov top, rubber disk, and Celtic stone. It is shown that they exhibit mixed dynamics of different nature; in particular, the mixed dynamics observed in the model of rubber disk is extremely difficult to distinguish from the conservative one.

中文翻译：

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三种类型的吸引子与刚体运动非完整模型的混合动力学

我们从拓扑动力学的角度调查了关于动态混沌理论的最新结果。我们介绍了三种动力学类型的概念：保守动力学，耗散动力学和混合动力学，还展示了这三种类型的吸引器和排斥器的几个简单示例。讨论了它们与其他已知类型的吸引器和排斥器（最大和最小）的异同。我们还提出了可逆系统混合动力学定性理论的要素。作为此类系统的示例，我们考虑了三种刚体运动的非完整模型：Suslov顶部，橡胶盘和凯尔特人的石头。结果表明，它们表现出不同性质的混合动力。尤其是，在橡胶盘模型中观察到的混合动力学很难与保守模型区分开。