On the structure of some typical singularities for implicit ordinary differential equations

Details On the structure of some typical singularities for implicit ordinary differential equations On the structure of some typical singularities for implicit ordinary differential equations

2000-07-07

arxiv.org/abs/math-ph/0007008v1

Physics

Mathematical Physics

20 LaTeX pages, 2 Latex figures

Scientific paper

We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives reduces to the singular surface where the theorem of uniqueness and existence is violated.A set of the singular solution is obtained for the case requiring the minimal number of additional conditions. The various types of singularities correspond to these cases. These ``turning'', ``intersection'' singularities appear in several physical applications.

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