含有真的弱几乎周期点系统的动力性状研究

项目名称： 含有真的弱几乎周期点系统的动力性状研究

项目编号： No.11261039

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 尹建东

作者单位： 南昌大学

项目金额： 30万元

中文摘要： 以已建立的弱几乎周期点的性质和理论为基础，对含有真的弱几乎周期点的系统，研究其拓扑熵的所有可能情况, 建立其具有正拓扑熵的充分条件(如可能为零熵的话)，探索其具有的混沌性状和拓扑传递属性，并研究三者之间的联系。 含有真的弱几乎周期点的系统一般认为是很复杂，对其拓扑熵，混沌性状和拓扑传递属性加以研究，不仅可以完善拓扑动力系统的基础理论，加深人们对弱几乎周期点的认识， 而且可以为以后的研究提供新的方法或思路。 因此对含有真的弱几乎周期点的系统的拓扑熵，混沌性状和拓扑传递属性加以研究具有重要理论意义和实际意义。

中文关键词： 弱几乎周期点；混沌；拓扑传递；拓扑熵；

英文摘要： Based on the properties and theories of weakly almost periodic points, we shall study what will happen for topological entropy of the systems with proper weakly almost periodic points, set up the sufficient condition for such systems to have positive topological entropy (if they may have zero topological entropy) and investigate whether the systems are chaotic and what topologically transitive properties the systems should have. Furthermore, we shall study the relationships among topological entropy, chaotic properties and topologically transitive properties for such a class of systems. In general, the systems with proper weakly almost periodic points are complex. The studies of topological entropy, chaotic properties and topologically transitive properties for such a class of systems not only can improve the basic theories of topological dynamical systems and deepen the understanding of weakly almost periodic points but also can offer some new metholds and ideas for our future reaserches. Thus, the studies of topological entropy, chaotic properties and topologically transitive properties for such a class of systems are of important significance in theory and reality.

英文关键词： Weakly almost periodic point；Chaos；Topological transtiivity；Topological entropy；