Normal Forms of the Degenerate Differential Autonomous and Non Autonomous Equations with the Maximal Jordan Chain of Length Two and Three
Standard methods of normal form construction are adapted for degenerate differential equations in the case of the existence of maximal length Jordan chain. For n=2 and 3 examples are considered. Some of indicated normal forms are obtained for non autonomous systems at the usage of determined in the article differential Jordan chains.
1. Vainberg M.M., Trenogin V.A. Theory of branching of solutions of non-linear equations. Noordhoof International Publishing, Leyden, 1974.
2. Sidorov N., Loginov B., Sinitsyn A., Falaleev M. Lyapunov – Schmidt Methods in Nonlinear Analysis and Applications. Dortrecht, Kluwer Academic Publ., 2002. 548 p.
3. Arnold V.I. Geometricheskie metody v teoriy obiknovennykh differentsialnykh uravneniy [Geometrical Methods in the Theory of Ordinary Differential Equations]. Мoscow, 1999.
4. Shui-Nee Chow, Chengzhi Li, Duo Wang. Normal Forms and Bifurcation of Planar Vector Fields. Cambridge University Press, 1994. 484 p.
5. Loginov B.V., Rousak Yu.B., Kim-Tyan L.R. Normal forms of the degenerate autonomous differential equations with the maximal Jordan chain and simple applications. Bulletin of South-Ural University, Series Mathematics, 2015, no 4.
6. Marszalek W. Fold Points and Singularity Induced Bifurcation in Inviscid Transonic Flow. Physics Letters A., 2012, vol. 376, issues 28-29, pp. 2032–2037, http://dx.doi.org/10.1016/j.physleta.2012.05.003
7. Elphick C., Tirapegui E., Brachet M.E., Coullet P., Iooss G. A Simple Global Characterization for Normal Forms of Singular Vector Fields. Physica 29D, North-Holland, Amsterdam, 1987, pp. 95–127