混沌动力系统Hausdorff周期律和概率周期律的关系定理(英文)

The Relation between the Periodicity of Chaotic Dynamical Systems in Hausdorff and Probability Spaces

在综合分析混沌动力系统概率测度渐进独立性和周期性的基础上,提出了混沌动力系统Hausdorff周期律和概率周期律的关系定理。该定理成功地跨越了确定性现象和随机现象间的鸿沟,揭示了Hausdorff周期律和概率周期律间的依存关系,它表明混沌动力系统的Hausdorff周期律是其概率周期律的一种表象。这一发现不仅清楚地解释了混沌动力系统Hausdorff周期律的非退化机理,而且对揭开混沌现象的本质至关重要。

The theorem describing the exact relationship between the periodicity of chaotic dynamical systems in Hausdorffand probability spaces is proposed. This theorem which is a constructive bridge between the deterministic and indeterministicphenomena shows that the periodic behavior of chaotic dynamical systems in probability spaces is the origin of their periodicityin Hausdorff metric spaces. This is why the periodicity of chaotic dynamical systems in Hausdorff metric spaces is non-degener-ated. It is very important to reveal the essence of chaos.