【摘要】 目的研究拓扑动力系统的动力性状。方法通过拓扑共轭和半共轭的方法,用加法机器来研究拓扑动力系统的动力性状。结果获得了拓扑动力系统(X,f)有一个子系统(Λ,f|Λ)与加法机器(Δα,fα)拓扑(半)共轭充分必要条件。结论类似于把符号动力系统拓扑共轭嵌入到给定拓扑动力系统,把加法机器拓扑共轭嵌入到复杂拓扑动力系,为研究复杂动力系统的动力性状提供了另一种方法。更多还原

【Abstract】 Aim To investigate the dynamical behavior and complexity of topological dynamical systems.Methods The adding machine is embedded into topological dynamical systems to explore various dynamical properties of these systems.Results A necessary and sufficient condition is established for the existence of a subsystem in the given topological dynamical system that is conjugate(resp.,semi-conjugate) to the adding achine.Conclusion Parallel to embedding the symbolic system into a given system,embedding the adding machine into the given system provides an alternative approach for exploring dynamical complexity of the given system.更多还原