### Straightforward expansion of non-autonomous integrals for quasi-conservative systems with one degree of freedom

#### N. V. Kovalev1

Annotation 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. quasiconservative system, nonautonomous integral, periodic solutions, limit cycles, action-angle variables, small-parameter expansion

1Postgraduate student of the Differential Equations Department, Moscow Aviation Institute (National Research University), Moscow; nick.kvlv@gmail.com

Citation: N. V. Kovalev, "[Straightforward expansion of non-autonomous integrals for quasi-conservative systems with one degree of freedom]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:3 (2016) 32–40 (In Russian)