Singularities of Implicit Differential Equations and Static Bifurcations

Reference: Computer Algebra in Scientific Computing - CASC 2013, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2013, Lecture Notes in Computer Science 8136, pp. 355-368

Description: This paper discusses geometric singularities of implicit ordinary differential equations from the point of view of Vessiot theory. It is shown that quasi-linear systems admit a special treatment leading to phenomena not present in the general case. These results are then applied to study static bifurcations of parametric ordinary differential equations.

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