The survey is devoted to the topological dynamics of maps defined on one-dimensional continua such as a closed interval, a circle, finite graphs (for instance, finite trees), or dendrites (locally connected continua without subsets homeomorphic to a circle). Connections between the periodic behaviour of trajectories, the existence of a horseshoe and homoclinic trajectories, and the positivity of topological entropy are investigated. Necessary and sufficient conditions for entropy chaos in continuous maps of an interval, a circle, or a finite graph, and sufficient conditions for entropy chaos in continuous maps of dendrites are presented. Reasons for similarities and differences between the properties of maps defined on the continua under consideration are analyzed. Extensions of Sharkovsky’s theorem to certain discontinuous maps of a line or an interval and continuous maps on a plane are considered.

Bibliography: 207 titles.

该调查致力于在一维连续体上定义的映射的拓扑动力学，例如闭区间、圆、有限图（例如，有限树）或树突（局部连接的连续体，没有与圆同胚的子集）。研究了轨迹的周期性行为、马蹄形和同宿轨迹的存在以及拓扑熵的正性之间的联系。给出了区间、圆、有限图的连续映射熵混沌的充要条件，以及枝晶连续映射熵混沌的充分条件。分析了在考虑的连续体上定义的地图属性之间的异同原因。

参考书目：207 个标题。