树突映射是动力系统的一个重要分支,在复动力学、生物学、生态学、生理学、物理学、经济学、控制论和计算机科学等许多自然科学中有着广泛的应用。该项目主要研究以下几个方面的内容:(1) 支点个数无限的树突上映射的P-R性质、中心和中心深度等系列问题。(2) 树突映射的吸引中心的拓扑结构等相关问题。(3)树突上非自治系统的 w-极限集的拓扑结构以及树突上非自治系统的等度连续性。(4)树突映射的混沌性、拓扑熵、 a-极限集和 r-极限集和非游荡集的拓扑结构等问题。

Dendrite map is an important branch of dynamical system, the application of its theory is rapidly broadening to various fields, such as complex dynamics, biology, ecology, physiology, physics, economics, control theory, computer science and so on. This project study mainly that: (1) The P-R properties, the depths of centres and the centres for maps of denrites with the number of branches is infinite. (2) The topological structure of the attracting centre of a dendrite map. (3) The topological structure of the set of ω-limit points and the equicontinuity of non-autonomous dynamic systems on dendrites. (4)The chaoses and the topological entropies of dendrite maps, and the topological structures of the sets of a-limit points, the sets of r-limit points and the non-wandering sets of dendrite maps.