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A Gentle Introduction to Quasi-periodic Phenomena

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Abstract

We give an elementary introduction to the theory of quasi-periodic oscillations based on their basic property of frequency incommensurability. First, we provide their brief mathematical description, examples from physics, and the visualization and measuring methods. We also propose a new simple technique for evaluating their degree of non-periodicity. The issues outlined in this article will be useful for instructors and physics undergraduates dealing with the modern theory of oscillations.

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Suggested Reading

  1. A Celletti and S Ferraz-Mello, Periodic, quasi-periodic and chaotic motions in celestial mechanics: theory and applications, Springer-Nature, 2006.

  2. Eric W. Weisstein, Kolmogorov-Arnold-Moser theorem, From MathWorld–A Wolfram Web Resource, https://mathworld.wolfram.com/Kolmogorov-Arnold-MoserTheorem.html.

  3. E Hopf, A mathematical example displaying features of turbulence, Comm. Pure Appl. Math., Vol.1, No.4, pp.303–322, 1948.

    Article  Google Scholar 

  4. C Corduneanu, Almost Periodic Oscillations and Waves, Springer-Verlag New York, 2009.

    Book  Google Scholar 

  5. H W Broer, G B Huitema, M B Sevryuk, Quasi-periodic Motions in Families of Dynamical Systems - Order Amidst Chaos - Introduction and Examples, Springer Berlin, 1996.

    Google Scholar 

  6. H Bohr, Almost Periodic Functions, American Mathematical Society, Reprint, 1947.

  7. Keith Briggs, Badly approximable, From MathWorld–A Wolfram Web Resource, created by Eric W. Weisstein, https://mathworld.wolfram.com/BadlyApproximable.html.

  8. W M Schmidt, On badly approximable numbers and certain games, Trans. Am. Math. Soc., Vol.123, pp.178–199, 1966.

    Article  Google Scholar 

  9. R Ben’ıtez, V J Bol’os and M E Ram’ırez, A wavelet-based tool for studying non-periodicity, Comput. Math. Appl., Vol.60, pp.634–641, 2010.

    Article  Google Scholar 

  10. Y Ni, K Turitsyn, H Baoyin and Li Junfeng, Entropy method of measuring and evaluating periodicity of quasi-periodic trajectories, Science China Physics, Mechanics and Astronomy Volume, Vol.61, p.064511, 2018.

    Article  Google Scholar 

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Correspondence to Vladimir Ivchenko.

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Vladimir Ivchenko is an associate professor in the Department of Natural Science Training of the Kherson State Maritime Academy. He holds a PhD in solid-state physics. His research interests are in theoretical physics, computational physics and physics education.

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Ivchenko, V. A Gentle Introduction to Quasi-periodic Phenomena. Reson 28, 1135–1144 (2023). https://doi.org/10.1007/s12045-023-1642-0

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  • DOI: https://doi.org/10.1007/s12045-023-1642-0

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