On the density of Birkhoff sums for Anosov diffeomorphisms  

作　　者：Shaobo Gan Yi Shi Mingyang Xia 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Science China Mathematics》2022年第2期319-330,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11771025 and 11831001);supported by National Natural Science Foundation of China(Grant Nos.12071007 and 11831001)。

摘　　要：Let f : M → M be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Holder continuous observation along periodic orbits. We show that if there are two Birkhoff sums distributed at both sides of zero, then the set of Birkhoff sums of all the periodic points is dense in R.

关 键 词：Anosov diffeomorphism Birkhoff sum periodic point NILMANIFOLD 

分 类 号：O19[理学—数学]