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Regular and Chaotic Dynamics, 2020, Volume 25, Issue 1, Pages 121–130
DOI: https://doi.org/10.1134/S1560354720010104 (Mi rcd1053) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Special issue: In honor of Valery Kozlov for his 70th birthday

Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems

Alexander A. Burovab, Anna D. Guermanc, Vasily I. Nikonovba

a Federal Research Center “Computer Science and Control”, Vavilova ul. 40, Moscow, 119333 Russia
b National Research University “Higher School of Economics”, Myasnitskaya ul. 20, Moscow, 101000 Russia
c Centre for Aerospace Science and Technologies, University of Beira Interior, Convento de Sto. António. 6201-001 Covilhã, Portugal
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DOI: https://doi.org/10.1134/S1560354720010104
Abstract: Invariant surfaces play a crucial role in the dynamics of mechanical systems separating regions filled with chaotic behavior. Cases where such surfaces can be found are rare enough. Perhaps the most famous of these is the so-called Hess case in the mechanics of a heavy rigid body with a fixed point.
We consider here the motion of a non-autonomous mechanical pendulum-like system with one degree of freedom. The conditions of existence for invariant surfaces of such a system corresponding to non-split separatrices are investigated. In the case where an invariant surface exists, combination of regular and chaotic behavior is studied analytically via the Poincaré – Mel'nikov separatrix splitting method, and numerically using the Poincaré maps.
Keywords: separatrices splitting, chaotic dynamics, invariant surface.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00335
Federación Española de Enfermedades Raras Centro-01- 0145-FEDER-000017
POCI-01-0145-FEDER-007718
This research is partially supported by RFBR, grants 18-01-00335, project EMaDeS (Centro-01- 0145-FEDER-000017), and the Portuguese Foundation for Science and Technologies via the Centre for Mechanical and Aerospace Science and Technologies, C-MAST, POCI-01-0145-FEDER-007718.
Received: 15.09.2019
Accepted: 15.12.2019
Bibliographic databases:
Document Type: Article
MSC: 70H07, 70K40, 70K55
Language: English
Citation: Alexander A. Burov, Anna D. Guerman, Vasily I. Nikonov, “Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems”, Regul. Chaotic Dyn., 25:1 (2020), 121–130
Citation in format AMSBIB
\Bibitem{BurGueNik20}
\by Alexander A. Burov, Anna D. Guerman, Vasily I. Nikonov
\paper Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 1
\pages 121--130
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\crossref{https://doi.org/10.1134/S1560354720010104}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85079753102}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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