Benjamin McKay
Published 2005-07-05, updated 2007-03-26Version 5
The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn out to provide an infinite dimensional family of integrable systems.
Comments: 29 pages, 1 figure, v.2 more citations, v.3 more examples, v.4 minor corrections, v.5 minor corrections
Normal Forms of second order Ordinary Differential Equations $y_{xx}=J(x,y,y_{x})$ under Fibre-Preserving Maps
The point equivalence problem for ordinary differential equations of the second order
Almost contact structures on the deformation space of rational curves in a 4-dimensional twistor space
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