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Time symmetries and in-period transformations. (English) Zbl 1221.34089

Summary: A theorem is proved which gives us the opportunity to investigate the properties of the Poincaré function of periodic differential systems.

MSC:

34C14 Symmetries, invariants of ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34C25 Periodic solutions to ordinary differential equations
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References:

[1] Mironenko, V. I., Reflecting Function and Periodic Solution of the Differential System (1986), Belgosuniver Press: Belgosuniver Press Minsk · Zbl 0607.34038
[2] Mironenko, V. I., Reflecting Function and Discussion of Many-Dimensional Differential System (2004), Gomel University: Gomel University Belarus · Zbl 1079.34518
[3] Mironenko, V. I.; Mironenko, V. V., The perturbations of the systems, which do not change time-symmetries and Poincaré’s map, Differ. Equ., 44, 10, 1347-1358 (2008) · Zbl 1194.34102
[4] Mironenko, V. I.; Mironenko, V. V., How to construct equivalent differential systems, Appl. Math. Lett., 22, 1356-1359 (2009) · Zbl 1173.35407
[5] Arnold, V. I., Ordinary Differential Equations (1984), Nauka: Nauka Moscow
[6] Hartman, Ph., Ordinary Differential Equations (1964), Johns Hopkins University: Johns Hopkins University New York, London, Sydney
[7] Mironenko, V. I., Linear Dependence of the Functions Along the Solutions of Differential Equations (1981), Belgosuniver Press: Belgosuniver Press Minsk · Zbl 0496.34001
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