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@article{TM_2006_254_a1, author = {N. B. Medvedeva}, title = {On the {Analytic} {Solvability} of the {Problem} of {Distinguishing} between {Center} and {Focus}}, journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova}, pages = {11--100}, publisher = {mathdoc}, volume = {254}, year = {2006}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TM_2006_254_a1/} }
TY - JOUR AU - N. B. Medvedeva TI - On the Analytic Solvability of the Problem of Distinguishing between Center and Focus JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 2006 SP - 11 EP - 100 VL - 254 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TM_2006_254_a1/ LA - ru ID - TM_2006_254_a1 ER -
N. B. Medvedeva. On the Analytic Solvability of the Problem of Distinguishing between Center and Focus. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Nonlinear analytic differential equations, Tome 254 (2006), pp. 11-100. http://geodesic.mathdoc.fr/item/TM_2006_254_a1/
[1] Arnold V.I., Ilyashenko Yu.S., “Obyknovennye differentsialnye uravneniya”, Dinamicheskie sistemy–1, Itogi nauki i tekhniki. Sovr. probl. matematiki. Fund. napr., 1, VINITI, M., 1985, 7–147 | MR
[2] Dumortier F., “Singularities of vector fields on the plane”, J. Diff. Equat., 23 (1977), 53–106 | DOI | MR | Zbl
[3] Ilyashenko Yu.S., Finiteness theorems for limit cycles, Transl. Math. Monogr., 94, Amer. Math. Soc., Providence (RI), 1991 | MR | Zbl
[4] Puankare A., O krivykh, opredelyaemykh differentsialnymi uravneniyami, Gostekhteorizdat, M.; L., 1947
[5] Lyapunov A.M., Obschaya zadacha ob ustoichivosti dvizheniya, Gostekhteorizdat, M.; L., 1950 | Zbl
[6] Moussu R., “Symétrie et forme normale des centres et foyers dégénérés”, Ergod. Theory and Dyn. Syst., 2 (1982), 241–251 | MR | Zbl
[7] Nemytskii V.V., Stepanov V.V., Kachestvennaya teoriya differentsialnykh uravnenii, Gostekhteorizdat, M.; L., 1949
[8] Bryuno A.D., Lokalnyi metod nelineinogo analiza differentsialnykh uravnenii, Nauka, M., 1979 | MR
[9] Berezovskaya F.S., Slozhnaya statsionarnaya tochka sistemy na ploskosti: struktura okrestnosti i indeks, Preprint ONTI NTsBI, Puschino, 1978 | MR
[10] Berezovskaya F.S., Medvedeva N.B., “Asimptotika preobrazovaniya monodromii osoboi tochki s fiksirovannoi diagrammoi Nyutona”, Tr. sem. im. I.G. Petrovskogo, 15 (1991), 156–177 | MR
[11] Berezovskaja F.S., Medvedeva N.B., “A complicated singular point of “center–focus” type and the Newton diagram”, Sel. Math., 13:1 (1994), 1–15
[12] Medvedeva N.B., “Glavnyi chlen asimptotiki preobrazovaniya monodromii: vychislenie po diagramme Nyutona”, Tr. MIAN, 213 (1997), 226–238 | MR | Zbl
[13] Berezovskaya F.S., Stepennye asimptotiki sistemy differentsialnykh uravnenii vtorogo poryadka, Preprint ONTI NTsBI, Puschino, 1976
[14] Medvedeva N.B., “Derevo razdutiya dlya vektornykh polei s fiksirovannoi diagrammoi Nyutona”, Vestn. MGU. Matematika, mekhanika, 1989, no. 1, 13–17 | MR | Zbl
[15] Arnold V.I., “O lokalnykh zadachakh analiza”, Vestn. MGU. Matematika, mekhanika, 1970, no. 2, 52–56 | Zbl
[16] Arnold V.I., “Algebraicheskaya nerazreshimost problemy ustoichivosti po Lyapunovu i problemy topologicheskoi klassifikatsii osobykh tochek analiticheskoi sistemy differentsialnykh uravnenii”, Funkts. anal. i ego pril., 4:3 (1970), 1–9 | MR
[17] Ilyashenko Yu.S., “Algebraicheski i analiticheski razreshimye lokalnye zadachi teorii obyknovennykh differentsialnykh uravnenii”, Tr. sem. im. I.G. Petrovskogo, 12 (1987), 118–136 | MR
[18] Ilyashenko Yu.S., “Memuar Dyulaka “O predelnykh tsiklakh” i smezhnye voprosy lokalnoi teorii differentsialnykh uravnenii”, UMN, 40:6 (1985), 41–78 | MR
[19] Ilyashenko Yu.S., “Analiticheskaya nerazreshimost problemy ustoichivosti i problemy topologicheskoi klassifikatsii osobykh tochek analiticheskikh sistem differentsialnykh uravnenii”, Mat. sb., 99:2 (1976), 162–175 | MR | Zbl
[20] Alekseev B.V., Problema razlicheniya tsentra i fokusa s tochki zreniya algebraicheskoi razreshimosti, NII upravleniya mashin i sistem, Perm, 1987, 29 pp.; Рук. деп. в ЦНИИТЭИ приборостроения 09.04.1987, No3728-пр.87
[21] Ilyashenko Yu.S., “Algebraicheskaya nerazreshimost i pochti algebraicheskaya razreshimost problemy tsentr–fokus”, Funkts. anal. i ego pril., 6:3 (1972), 30–37 | MR | Zbl
[22] Dyulak G., O predelnykh tsiklakh, Nauka, M., 1980 | MR
[23] Krushina N.P., Medvedeva N.B., “Ob analiticheskoi razreshimosti problemy ustoichivosti v nekotorykh klassakh monodromnykh rostkov”, Dif. uravneniya, 37:9 (2001), 1168–1176 | MR
[24] Medvedeva N.B., Krushina N.P., “Analiticheskaya razreshimost problemy ustoichivosti v nekotorykh klassakh monodromnykh rostkov”, Differentsialnye i integralnye uravneniya, Tez. dokl. Mezhdunar. nauch. konf. (Chelyabinsk, 22–26 iyunya 1999 g.), Chelyabinsk, 1999, 79
[25] Medvedeva N.B., Analiticheskaya razreshimost problemy razlicheniya tsentra i fokusa v nekotorykh klassakh vektornykh polei so slozhnoi monodromnoi osoboi tochkoi, Tr. In-ta matematiki i mekhaniki UrO RAN, 8, no. 2, 2002
[26] Medvedeva N.B., “Problema razlicheniya tsentra i fokusa v klasse rostkov s dvumya rebrami diagrammy Nyutona”, Vestn. ChelGU. Cer. 3, 2003, no. 3, 86–110 | MR
[27] Medvedeva N.B., “Kriterii monodromnosti osoboi tochki vektornogo polya na ploskosti”, Algebra i analiz, 13:2 (2001), 130–150 | MR
[28] Medvedeva N.B., Mazaeva E.V., “Dostatochnoe uslovie fokusa dlya monodromnoi osoboi tochki”, Tr. Mosk. mat. o-va, 63 (2002), 87–114 | MR | Zbl
[29] Gantmakher F.R., Teoriya matrits, Nauka, Fizmatlit, M., 1988 | MR | Zbl
[30] Gorin E.A., “Ob asimptoticheskikh svoistvakh mnogochlenov i algebraicheskikh funktsii ot neskolkikh peremennykh”, UMN, 16:1 (1961), 91–117 | MR