On the density of Birkhoff sums for Anosov diffeomorphisms

Let f : M → M be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Hölder 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.

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Bibliographic Details
Published inScience China. Mathematics Vol. 65; no. 2; pp. 319 - 330
Main Authors Gan, Shaobo, Shi, Yi, Xia, Mingyang
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.02.2022
Springer Nature B.V
Subjects
Applications of Mathematics
Isomorphism
Mathematics
Mathematics and Statistics
Orbits
Sums
Birkhoff sum
periodic point
Anosov diffeomorphism
nilmanifold
37D05
37D20
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Summary:Let f : M → M be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Hölder 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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-020-1858-9