Geodesic
Dynamic quadrangles and isochronous oscillations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 381-384 Cet article a éte moissonné depuis la source Math-Net.Ru

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Integral formulas are exposed which express a relation between the movement times of transversal plain flows along the opposite sides of the “dynamic quadrangles” generated by the flows. In the formulas, the main role is played by the Poisson bracket. An application is presented to the theory of isochronous oscillations.
Keywords: dynamic quadrangles
Mots-clés : Poisson brackets, isochronous oscillations. 
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     title = {Dynamic quadrangles and isochronous oscillations},
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V. V. Ivanov. Dynamic quadrangles and isochronous oscillations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 381-384. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a26/

[1] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989 | MR

[2] J. Chavarriga, M. Sabatiny, “A survey of isochronous centers”, Qualitative Theory of Dynamical Systems, 1:1 (1999), 1–70 | DOI | MR

[3] Villarini M., “Regularity properties of the period function near a centre of planar vector fields”, Nonlinear Analisys. T.M.A, 19 (1992), 787–803 | DOI | MR | Zbl

[4] A. Algaba, E. Freire, E. Gamero, “Isochronicity via normal form”, Qual. Theory Dyn. Syst., 1:2 (2000), 133–156 | DOI | MR | Zbl

[5] V. V. Ivanov, “Dinamicheskie chetyrekhugolniki transversalnykh vektornykh polei i skobki Puassona”, Mezhdunarodnaya konferentsiya, posvyaschennaya 100-letiyu so dnya rozhdeniya S. L. Soboleva. Tezisy dokladov (Novosibirsk, Rossiya, 5–12 oktyabrya, 2008), 140