Abstract
We consider an autonomous system of ordinary differential equations, which is solved with respect to derivatives. To study local integrability of the system near a degenerate stationary point, we use an approach based on Power Geometry method and on the computation of the resonant normal form. For a planar 5-parametric example of such system, we found the complete set of necessary and sufficient conditions on parameters of the system for which the system is locally integrable near a degenerate stationary point.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bruno, A.D., Edneral, V.F.: Algorithmic analysis of local integrability. Dokl. Akademii Nauk 424(3), 299–303 (2009) (in Russian); Doklady Mathem. 79(1), 48–52 (2009) (in English)
Bruno, A.D.: Power Geometry in Algebraic and Differential Equations. Fizmatlit, Moscow (1998) (in Russian); Elsevier Science, Amsterdam (2000) (in English)
Bruno, A.D.: Local Methods in Nonlinear Differential Equations, Nauka, Moscow (1979) (in Russian); Springer, Berlin (1989) (in English)
Bruno, A.D.: Analytical form of differential equations (I,II). Trudy Moskov. Mat. Obsc. 25, 119–262 (1971); 26, 199–239 (1972) (in Russian); Trans. Moscow Math. Soc. 25, 131–288; 26, 199–239 (1972) (in English)
Algaba, A., Gamero, E., Garcia, C.: The integrability problem for a class of planar systems. Nonlinearity 22, 395–420 (2009)
Siegel, C.L.: Vorlesungen über Himmelsmechanik. Springer, Berlin (1956) (in German); Fizmatlit, Moscow (1959) (in Russian)
Edneral, V.F.: On algorithm of the normal form building. In: Ganzha, et al. (eds.) Proc. CASC 2007. LNCS, vol. 4770, pp. 134–142. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bruno, A., Edneral, V. (2009). On Integrability of a Planar ODE System Near a Degenerate Stationary Point. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-04103-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04102-0
Online ISBN: 978-3-642-04103-7
eBook Packages: Computer ScienceComputer Science (R0)