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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.09496 |
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| _version_ | 1866929500973957120 |
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| author | Tong, Zhicheng Li, Yong |
| author_facet | Tong, Zhicheng Li, Yong |
| contents | In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to the quasiperiodic and almost periodic dynamical systems respectively, under certain balance between the nonresonant condition and the decay rate of the Fourier coefficients. Diophantine rotations with finite and infinite dimensions are provided as examples. For the first time, we prove the universality of exponential convergence and arbitrary polynomial convergence in the quasiperiodic case and almost periodic case under analyticity respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09496 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exponential convergence of weighted Birkhoff average Tong, Zhicheng Li, Yong Dynamical Systems 37A25, 37A45 In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to the quasiperiodic and almost periodic dynamical systems respectively, under certain balance between the nonresonant condition and the decay rate of the Fourier coefficients. Diophantine rotations with finite and infinite dimensions are provided as examples. For the first time, we prove the universality of exponential convergence and arbitrary polynomial convergence in the quasiperiodic case and almost periodic case under analyticity respectively. |
| title | Exponential convergence of weighted Birkhoff average |
| topic | Dynamical Systems 37A25, 37A45 |
| url | https://arxiv.org/abs/2205.09496 |