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Regular and Chaotic Dynamics, 2001, Volume 6, Issue 1, Pages 53–94
DOI: https://doi.org/10.1070/RD2001v006n01ABEH000166 (Mi rcd834) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Study of the Double Mathematical Pendulum — IV. Quantitative Bounds on Values of the System Parameters when the Homoclinic Transversal Intersections Exist

A. V. Ivanov

Physics Department, St.-Petersburg State University, Ulyanov str., 1, build, 1, Petrodvorets, St.-Petersburg, 198604, Russia
Citations (1)
DOI: https://doi.org/10.1070/RD2001v006n01ABEH000166
Abstract: We consider the double mathematical pendulum in the limit of small ratio of pendulum masses. Besides we assume that values of other two system parameters are close to the degenerate ones (i.e. zero or infinity). In these limit cases we prove asymptotic formulae for the homoclinic invariant of some special chosen homoclinic trajectories and obtain quantitative bounds on values of the system parameters when these formulae are valid.
Received: 14.11.2000
Bibliographic databases:
Document Type: Article
MSC: 34C15, 70H08, 70K70
Language: English
Citation: A. V. Ivanov, “Study of the Double Mathematical Pendulum — IV. Quantitative Bounds on Values of the System Parameters when the Homoclinic Transversal Intersections Exist”, Regul. Chaotic Dyn., 6:1 (2001), 53–94
Citation in format AMSBIB
\Bibitem{Iva01}
\by A. V. Ivanov
\paper Study of the Double Mathematical Pendulum — IV. Quantitative Bounds on Values of the System Parameters when the Homoclinic Transversal Intersections Exist
\jour Regul. Chaotic Dyn.
\yr 2001
\vol 6
\issue 1
\pages 53--94
\mathnet{http://mi.mathnet.ru/rcd834}
\crossref{https://doi.org/10.1070/RD2001v006n01ABEH000166}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1825428}
\zmath{https://zbmath.org/?q=an:1064.70019}
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