Abstract
We study the generalized quasiperiodically forced circle map \(f:\mathbb {T}^{m}\times \mathbb {T}^{1}\rightarrow \mathbb {T}^{m}\times \mathbb {T}^{1}\), which is a natural generalization of the quasiperiodically forced circle map. Our main aim is to show that for each \(\rho \) in the interior of the fibred rotation set, there is a minimal set such that each orbit on the minimal set is \(\rho \)-bounded.
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Acknowledgements
We are grateful to the anonymous referees for their helpful suggestions. Tong Zhou was supported by the National Natural Science Foundation of China(12201446), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(22KJB110005), and the Shuangchuang Program of Jiangsu Province (JSSCBS20220898).
Funding
1. National Natural Science Foundation of China, 12201446; 2. Natural Science Foundation of the Jiangsu Higher Education Institutions of China, 22KJB110005; 3. Shuangchuang Program of Jiangsu Province, JSSCBS20220898.
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Tong Zhou wrote the main manuscript text. Tong Zhou and Guangxun sun reviewed the manuscript.
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Zhou, T., Sun, G. \(\rho \)-bounded orbits and minimal sets for generalized quasiperiodically forced circle maps. Anal.Math.Phys. 14, 60 (2024). https://doi.org/10.1007/s13324-024-00916-z
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DOI: https://doi.org/10.1007/s13324-024-00916-z