Generalized Wilczynski invariants for non-linear ordinary differential equations

Details Generalized Wilczynski invariants for non-linear ordinary differential equations Generalized Wilczynski invariants for non-linear ordinary differential equations

2007-02-09

arxiv.org/abs/math/0702251v2

Proceedings of the IMA summer program, Minneapolis, MN, USA, July 17--August 4, 2006. New York, NY: Springer. The IMA Volumes

Mathematics

Differential Geometry

18 pages; corrected typos, added reference

Scientific paper

We show that classical Wilczynski--Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We explore geometric structures associated with equations that have vanishing generalized Wilczynski invariants and establish relationship of such equations with deformation theory of rational curves on complex algebraic surfaces.

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