Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SJIM_2008_11_1_a2, author = {E. P. Volokitin}, title = {{\CYRD}{\cyro}{\cyrs}{\cyrt}{\cyra}{\cyrt}{\cyro}{\cyrch}{\cyrn}{\cyrery}{\cyre} {\cyru}{\cyrs}{\cyrl}{\cyro}{\cyrv}{\cyri}{\cyrya} {\cyrc}{\cyre}{\cyrn}{\cyrt}{\cyrr}{\cyra} {\cyrd}{\cyrl}{\cyrya} {\cyrn}{\cyre}{\cyrk}{\cyro}{\cyrt}{\cyro}{\cyrr}{\cyrery}{\cyrh} {\cyrk}{\cyrl}{\cyra}{\cyrs}{\cyrs}{\cyro}{\cyrv} {\cyrp}{\cyro}{\cyrl}{\cyri}{\cyrn}{\cyro}{\cyrm}{\cyri}{\cyra}{\cyrl}{\cyrsftsn}{\cyrn}{\cyrery}{\cyrh} {\cyrs}{\cyro}{\cyrv}{\cyre}{\cyrr}{\cyrsh}{\cyre}{\cyrn}{\cyrn}{\cyro} {\cyri}{\cyrz}{\cyro}{\cyrh}{\cyrr}{\cyro}{\cyrn}{\cyrn}{\cyrery}{\cyrh} {\cyrs}{\cyri}{\cyrs}{\cyrt}{\cyre}{\cyrm}}, journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki}, pages = {37--45}, publisher = {mathdoc}, volume = {11}, number = {1}, year = {2008}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SJIM_2008_11_1_a2/} }
TY - JOUR AU - E. P. Volokitin TI - Достаточные условия центра для некоторых классов полиномиальных совершенно изохронных систем JO - Sibirskij žurnal industrialʹnoj matematiki PY - 2008 SP - 37 EP - 45 VL - 11 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJIM_2008_11_1_a2/ LA - ru ID - SJIM_2008_11_1_a2 ER -
E. P. Volokitin. Достаточные условия центра для некоторых классов полиномиальных совершенно изохронных систем. Sibirskij žurnal industrialʹnoj matematiki, Tome 11 (2008) no. 1, pp. 37-45. http://geodesic.mathdoc.fr/item/SJIM_2008_11_1_a2/
[1] Chavarriga J., Sabatini M., “A survey of isochronous centers”, Qualitative Theory of Dynam. Systems, 1:1 (1999), 1–70 | DOI | MR
[2] Algaba A., Reyes M., Bravo A., “Geometry of the uniformly isochronous centers with polynomial commutators”, Differential Equations Dynam. Systems, 10:3–4 (2002), 257–275 | MR | Zbl
[3] Algaba A., Reyes M., “Centers with degenerate infinity and their commutators”, J. Math. Anal. Appl., 78:1 (2003), 109–124 | DOI | MR
[4] Algaba A., Reyes M., “Computing center conditions for vector fields with constant angular speed”, J. Comput. Appl. Math., 154:1 (2003), 143–159 | DOI | MR | Zbl
[5] Conti R., “Centers of planar polynomial systems. A review”, Matematiche, 53:2 (1998), 207–240 | MR
[6] Cherkas L. A., “O chisle predelnykh tsiklov odnoi avtonomnoi sistemy vtorogo poryadka”, Differents. uravneniya, 12:5 (1976), 944–946 | MR | Zbl
[7] Schlomiuk D., “Algebraic and geometric aspects of the theory of polynomial vector fields”, Bifurcations and Periodic Orbits of Vector fields (Montréal, July 13–24, 1992), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 408, Kluwer Acad. Publ., Dordrecht, 1993, 429–467 | MR | Zbl
[8] Amelkin V. V., Lukashevich N. A., Sadovskii A. P., Nelineinye kolebaniya v sistemakh vtorogo poryadka, Izd-vo Belorus. gos. un-ta, Minsk, 1982 | MR
[9] Giné J., “The center problem for a linear center perturbed by homogeneous polynomials”, Acta. Math. Sin., 22:6 (2006), 1613–1620 | DOI | MR | Zbl
[10] Nemytskii V. V., Stepanov V. V., Kachestvennaya teoriya differentsialnykh uravnenii, Gostezkhizdat, M., L., 1949
[11] Sabatini M., “Characterizing isochronous centres by Lie brackets”, Differential Equations Dynam. Systems, 5:1 (1997), 91–99 | MR | Zbl
[12] Devlin J., “Coexisting isochronous and nonisochronous centres”, Bull. London Math. Soc., 28:5 (1996), 495–500 | DOI | MR | Zbl
[13] Volokitin E. P., Ivanov V. V., “Izokhronnost i kommutiruemost vektornykh polei”, Sib. mat. zhurn., 40:1 (1999), 30–48 | MR | Zbl
[14] Conti R., “Uniformly isochronous centers of polynomial systems in $R^2$”, Differential Equations, Dynamical Systems, and Control Science, Lect. Notes Pure and Appl. Math., 152, Marcel Dekker, New York, 1994, 21–31 | MR | Zbl
[15] Volokitin E. P., “Center conditions for a simple class of a quintic systems”, Internat. J. Math. Math. Sci., 29:11 (2002), 625–632 | DOI | MR | Zbl
[16] Algaba A., Reyes M., Bravo A., “Uniformly isochronous quintic planar vector field”, Internat. Conf. Differential Equations, Proc. Conf. Equadiff 99, V. 2 (Berlin, August 1–7, 1999), World Scientific, Singapore, 2000, 1415–1417 | MR | Zbl
[17] Collins C. B., “Poincaré's reversibility conditions”, J. Math. Anal. Appl., 259:1 (2001), 168–187 | DOI | MR | Zbl
[18] Mazzi L., Sabatini M., “Commutators and linearizations of isochronous centers”, Atti Acad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 11:2 (2000), 81–98 | MR | Zbl