Let $(X,\mathcal{F})$ be a nonautonomous dynamical system and μ be a Borel measure on X with a full support. The purpose of this paper is to introduce the concepts of large deviations theorem and expansive measure for nonautonomous discrete systems and investigate the dynamics of nonautonomous dynamical systems with the large deviations theorem. Actually, it is proved that $(X,\mathcal{F})$ is ergodicaly sensitive if the pair $(\mathcal{F},\mu )$ satisfies the large deviations theorem and $(X,\mathcal{F})$ is topologically strongly ergodic; $(X,\mathcal{F})$ is topologically ergodic if the pair $(\mathcal{F},\mu )$ satisfies the large deviations theorem in a sequence of positive integers; μ is expansive if the pair $(\mathcal{F},\mu )$ satisfies the large deviations theorem and $(X,\mathcal{F})$ is topologically strongly ergodic and each measurable set with positive measure with respect to μ has a nonempty interior.

让 $(X,\mathcal{F})$是一个非自治动力系统，μ是X上有完全支持的 Borel 测度。本文的目的是介绍非自治离散系统的大偏差定理和扩张测度的概念，并利用大偏差定理研究非自治动力系统的动力学。事实证明，$(X,\mathcal{F})$ 如果该对是遍历敏感的 $(\mathcal{F},\mu )$ 满足大偏差定理并且 $(X,\mathcal{F})$ 在拓扑上是强遍历的； $(X,\mathcal{F})$ 如果对是拓扑遍历的 $(\mathcal{F},\mu )$满足正整数序列的大偏差定理；μ是膨胀的，如果对$(\mathcal{F},\mu )$ 满足大偏差定理并且 $(X,\mathcal{F})$是拓扑强遍历的，并且每个对μ具有正测度的可测集都有一个非空的内部。