Geodesic
Straightforward expansion of non-autonomous integrals for quasi-conservative systems with one degree of freedom
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 3, pp. 32-40

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Quasi-conservative stationary systems with one degree of freedom are considered. Straightforward expansion of non-autonomous integrals for quasi-conservative systems is studied and analyticity of such integrals by small parameter is discussed. Method for constructing a set of non-autonomous integrals for quasi-conservative systems in action-angle variables is proposed. Criterion of closed orbits’ existence is obtained in terms of non-autonomous integrals. This criterion is used to estimate the number of limit cycles for one class of Lienard's equation.
Keywords: quasiconservative system, nonautonomous integral, periodic solutions, small-parameter expansion.
Mots-clés : limit cycles, action-angle variables 
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     author = {N. V. Kovalev},
     title = {Straightforward expansion of non-autonomous integrals for quasi-conservative systems with one degree of freedom},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {32--40},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a2/}
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N. V. Kovalev. Straightforward expansion of non-autonomous integrals for quasi-conservative systems with one degree of freedom. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 3, pp. 32-40. http://geodesic.mathdoc.fr/item/SVMO_2016_18_3_a2/