Abstract
We consider systems of the form \(\dot{x}=-y-P(x,y)\), \(\dot{y}=x+Q(x,y)\), where \(P\) and \(Q\) are functions holomorphic at the origin whose power series expansions in \(x\) and \(y\) do not contain free and linear terms and which satisfy the Cauchy–Riemann conditions. The maximum orders of the strong general isochronism and the strong partial (with given initial polar angle) isochronism are determined for systems in a fairly broad subclass of such systems.
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REFERENCES
Amel’kin, V.V. and Kalitin, B.S., Nelineinye izokhronnye i impul’snye kolebaniya v dinamicheskikh sistemakh vtorogo poryadka (Nonlinear Isochronous and Pulsed Vibrations in Second-Order Dynamical Systems), Minsk: Belarus. Gos. Univ., 2008.
Abdullaev, N., On the isochronicity under nonlinear vibrations, Tr. Tajikistan Uchit. Inst. im. S.S. Aini, 1954, no. 2, pp. 71–78.
Amel’kin, V.V. and Chin Jan Dang, On strong isochronicity of Cauchy–Riemann systems, Vestsi Nats. Akad. Navuk Belarusi. Ser. Fiz.-Mat. Navuk, 1993, no. 2, pp. 26–30.
Amel’kin, V.V., On one conjecture in the theory of isochronous Liénard systems, Differ. Equations, 2017, vol. 53, no. 10, pp. 1247–1253.
Amel’kin, V.V. and Dolićanin–Ðekić, D., On the higher-order strong isochronism of Cauchy-Riemann systems with homogeneous polynomial perturbations of a linear center, Differ. Equations, 2016, vol. 52, no. 5, pp. 667–671.
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Translated by V. Potapchouck
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Dolićanin–Ðekić, D. Higher-Order Strong Isochronism of Cauchy–Riemann Systems with Holomorphic Perturbations of a Linear Center. Diff Equat 56, 185–189 (2020). https://doi.org/10.1134/S0012266120020044
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DOI: https://doi.org/10.1134/S0012266120020044