Geodesic
Stability of monodromic singular points of planar dynamical systems with a fixed Newton diagram
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 34-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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The second term of asymptotics of the monodromy map of the monodromic singular point is calculated for some class of vector fields in the plane with the Newton diagram having two even edges. In this case the principal term of the monodromy map is identical. The result obtained gives the sufficient condition for a singular point to be a focus.
Mots-clés : monodromic singular point, monodromy map
Keywords: Newton diagram, resolution of singularities. 
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A. S. Voronin; N. B. Medvedeva. Stability of monodromic singular points of planar dynamical systems with a fixed Newton diagram. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 34-49. http://geodesic.mathdoc.fr/item/VUU_2009_3_a3/

[1] Arnold V. I., Ilyashenko Yu. S., “Obyknovennye differentsialnye uravneniya”, Dinamicheskie sistemy – 1, Sovremennye problemy matematiki. Fundamentalnye napravleniya. Itogi nauki i tekhniki, 1, VINITI AN SSSR, M., 1985, 7–140 | MR

[2] Medvedeva N. B., “Glavnyi chlen preobrazovaniya monodromii monodromnoi osoboi tochki lineen”, Sibirskii matematicheskii zhurnal, 33:2 (1992), 116–124 | MR | Zbl

[3] Berezovskaya F. S., Medvedeva N. B., “Asimptotika preobrazovaniya monodromii osoboi tochki s fiksirovannoi diagrammoi Nyutona”, Trudy seminara imeni I. G. Petrovskogo, no. 15, 1991, 156–177 | MR

[4] Medvedeva N., Batcheva E., “The second term of the asymptotics of monodromy map in case of two even edges of the Newton diagram”, Conference Proceedings of the 6-th Colloquium on the Qualitative Theory of Differential Equations. Szeged, EJQTDE, 19, 2000, 1–15 http://www.math.u-szeged.hu/ejqtde/ | MR

[5] Voronin A. S., Medvedeva N. B., “Asimptotika preobrazovaniya monodromii v sluchae dvukh chetnykh reber diagrammy Nyutona”, Vestnik ChelGU. Ser. 3. Matematika. Mekhanika. Informatika. Chelyabinsk, 2006, no. 1, 36–48 | MR

[6] Medvedeva N. B., “Ob analiticheskoi razreshimosti problemy razlicheniya tsentra i fokusa”, Trudy MIRAN im. V. A. Steklova, 254, 1996, 11–100 | MR

[7] Adamar Zh., Zadacha Koshi dlya lineinykh uravnenii s chastnymi proizvodnymi giperbolicheskogo tipa, Nauka, M., 1978, 352 pp. | MR

[8] Dyulak A., O predelnykh tsiklakh, Nauka, M., 1980, 157 pp. | MR