1·Ergodic theorems and the existence of invariant measures are two major topics in Ergodic theory.
遍历定理和不变测度的存在性是遍历理论中的二个基本研究主题。
2·Lindenstrauss, the ICM citation says, "has made far-reaching advances in ergodic theory," which studies the statistical behavior of dynamical systems.
国际数学联盟在颁奖辞中称Lindenstrauss在遍历理论方面取得了意义深远的进展，遍历理论是用于研究动力系统统计行为的数学分支。
3·Roughly speaking, dynamical systems consist of differential dynamical system, topological dynamical system, infinite dimensional dynamical system, complex dynamical system and ergodic theory etc.
今天的动力系统大致可分为微分动力系统、拓扑动力系统、无穷维动力系统、复动力系统、遍历论等方向。