大偏差定理与初值敏感性(英文)

The Large Deviations Theorem and Sensitive Dependence on Initial Conditions

本文讨论了动力系统的统计性质和动力性质的某些关系.对于紧致度量空间X上的连续自映射f,我们证明了:如果f满足大偏差定理,那么f是初值敏感的当且仅当f不是极小等度连续的.

In this paper, some relations between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X to itself, we show that if f satisfies the large deviations theorem,then f is sensitive dependence on initial conditions if and only if f is not minimally equicontinuous.