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Pointwise Ergodic Theorems for Higher Levels of Mixing
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- We prove strengthenings of the Birkhoff Ergodic Theorem for weakly mixing and strongly mixing measure preserving systems. We show that our pointwise theorem for weakly mixing systems is strictly stronger than the Wiener-Wintner Theorem. We also show that our pointwise Theorems for weakly mixing and strongly mixing systems characterize weakly mixing systems and strongly mixing systems respectively. The methods of this paper also allow one to prove an enhanced pointwise ergodic theorem for other levels of the ergodic hierarchy such as ergodicity and mild mixing but not K-mixing. The author plans to include these additional pointwise ergodic theorems in his thesis.<br />Comment: This paper is set to appear in Studia Mathematica
- Subjects :
- Pointwise
Pure mathematics
Mathematics::Dynamical Systems
Hierarchy (mathematics)
General Mathematics
Ergodicity
Dynamical Systems (math.DS)
Measure (mathematics)
37A25, 37A30, 37A05, 28D05
Pointwise ergodic theorem
FOS: Mathematics
Ergodic theory
Mathematics - Dynamical Systems
Mixing (physics)
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....64ec1bfd494db6944339658f1c3a639b
- Full Text :
- https://doi.org/10.48550/arxiv.2107.07861