半群中的Lipschitz各态历经和广义各态历经

The Lipschitz ergodicity and generalized ergodicity of semigroups

本文利用链回复性研究连续映射迭代形成的半群上Lipschitz各态历经和广义各态历经,分别给出Lipschitz各态历经和广义各态历经的充分必要条件,并举例说明各态历经、广义各态历经和Lipschitz各态历经性的关系.

In this paper, the semigroup is defined by the continuous transformation on the compact metric space. We use the chain recurrence to study the Lipschitz ergodicity and generalized ergodicity. Some criterions for a system to be Lipschitz ergodic or generalized ergodic are given. At last, we illustrate the relationship between ergodicity, generalized ergodicity and Lipschitz ergodicity.