Uniform and Semi-uniform Convergence for Discontinuous Skew-product Transformation and Observation  

作　　者：Xia PAN Zuo Huan ZHENG Zhe ZHOU 

机构地区：[1]College of Liberal Arts and Sciences,National University of Defense Technology,Changsha 410073,P.R.China [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China [3]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,P.R.China [4]ollege of Mathematics and Statistics,Hainan Normal University,Haikou 571158,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第2期333-344,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(NSFC)(Grant Nos.11671382 and 11301512);Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182);CAS Key Project of Frontier Sciences(Grant No.QYZDJ-SSW-JSC003);National Center for Mathematics and Interdisciplinary Sciences。

摘　　要：In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation and observation function are ignorable in some measure-theoretical sense. The theorems extend the classical results which have been established for continuous transformations and continuous observation functions.

关 键 词：Skew-product transformation uniform ergodicity semi-uniform ergodicity 

分 类 号：O174[理学—数学]