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Regular and Chaotic Dynamics, 2013, Volume 18, Issue 6, Pages 585–599
DOI: https://doi.org/10.1134/S1560354713060026 (Mi rcd150) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Stable Periodic Solutions in the Forced Pendulum Equation

Rafael Ortega

Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Citations (6)
References:
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DOI: https://doi.org/10.1134/S1560354713060026
Abstract: Consider the pendulum equation with an external periodic force and an appropriate condition on the length parameter. It is proved that there exists at least one stable periodic solution for almost every external force with zero average. The stability is understood in the Lyapunov sense.
Keywords: Lyapunov stability, forced pendulum, prevalence, periodic solution, regular value, discriminant.
Funding agency Grant number
Ministerio de Ciencia e Innovación de España MTM 2011-23652
Supported by project MTM 2011-23652, Ministerio de Ciencia e Innovación, Spain.
Received: 15.05.2013
Accepted: 04.10.2013
Bibliographic databases:
Document Type: Article
MSC: 34D20, 34C15, 34C25, 37C25, 58K05
Language: English
Citation: Rafael Ortega, “Stable Periodic Solutions in the Forced Pendulum Equation”, Regul. Chaotic Dyn., 18:6 (2013), 585–599
Citation in format AMSBIB
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\paper Stable Periodic Solutions in the Forced Pendulum Equation
\jour Regul. Chaotic Dyn.
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\vol 18
\issue 6
\pages 585--599
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Linking options:
  • https://www.mathnet.ru/eng/rcd150
  • https://www.mathnet.ru/eng/rcd/v18/i6/p585
    • This publication is cited in the following 6 articles:
    1. Yanxia Deng, Daniel Offin, “Stability of periodic orbits by Conley-Zehnder index theory”, Journal of Differential Equations, 314 (2022), 473  crossref
    2. F. Wang, J. Chu, Z. Liang, “Prevalence of stable periodic solutions in the forced relativistic pendulum equation”, Discrete Contin. Dyn. Syst.-Ser. B, 23:10 (2018), 4579–4594  crossref  mathscinet  zmath  isi  scopus
    3. Z. Liang, Zh. Zhou, “Stable and unstable periodic solutions of the forced pendulum of variable length”, Taiwan. J. Math., 21:4 (2017), 791–806  crossref  mathscinet  zmath  isi  scopus
    4. J. Chu, F. Wang, “Prevalence of stable periodic solutions for duffing equations”, J. Differ. Equ., 260:11 (2016), 7800–7820  crossref  mathscinet  zmath  isi  scopus
    5. A. Boscaggin, R. Ortega, F. Zanolin, “Subharmonic solutions of the forced pendulum equation: a symplectic approach”, Arch. Math., 102:5 (2014), 459–468  crossref  mathscinet  zmath  isi  scopus
    6. R. Ortega, “A forced pendulum equation without stable periodic solutions of a fixed period”, Port Math., 71:3-4 (2014), 193–216  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:39
     
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