Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold

被引：120
作者：
Leibman, A [1 ]
机构：
[1] Ohio State Univ, Dept Math, Columbus, OH 43221 USA
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2005年 / 25卷
关键词：
D O I：
10.1017/S0143385704000215
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that the orbit of a point on a compact nilmanifold X under the action of a polynomial sequence of translations on X is well distributed on the union of several sub-nilmanifolds of X. This implies that the ergodic averages of a continuous function on X along a polynomial sequence of translations on X converge pointwise.
引用
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页码：201 / 213
页数：13
相关论文
共 13 条
[1]  
[Anonymous], 1963, ANN MATH STUDIES
[2]   A nilpotent Roth theorem [J].
Bergelson, V ;
Leibman, A .
INVENTIONES MATHEMATICAE, 2002, 147 (02) :429-470
[3]  
Furstenberg H, 1981, Recurrence in ergodic theory and combinatorial number theory
[4]   Multiple recurrence theorem for measure preserving actions of a nilpotent group [J].
Leibman, A .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 1998, 8 (05) :853-931
[5]   MULTIPLE RECURRENCE THEOREM FOR NILPOTENT GROUP-ACTIONS [J].
LEIBMAN, A .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 1994, 4 (06) :648-659
[6]   ON A NILMANIFOLD MINIMAL PARTS ASSOCIATED WITH A TRANSLATION ARE UNIQUELY ERGODIC [J].
LESIGNE, E .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1991, 11 :379-391
[7]  
Maltsev A. I., 1949, Izv. Akad. Nauk SSSR Ser. Mat., V13, P9
[8]  
Montgomery D., 1955, TOPOLOGICAL TRANSFOR
[9]   ERGODIC PROPERTIES OF AFFINE TRANSFORMATIONS AND FLOWS ON NILMANIFOLDS [J].
PARRY, W .
AMERICAN JOURNAL OF MATHEMATICS, 1969, 91 (03) :757-&
[10]  
Parry W., 1970, Bull. London Math. Soc., V2, P37
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