Geodesic
Geometry of third order ODE systems
Archivum mathematicum, Tome 46 (2010) no. 5, pp. 351-361.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application.
Classification : 17B56, 34A26, 53B15
Keywords: geometry of ordinary differential equations; normal Cartan connections, cohomology of Lie algebras 
@article{ARM_2010__46_5_a5,
     author = {Medvedev, Alexandr},
     title = {Geometry of third order {ODE} systems},
     journal = {Archivum mathematicum},
     pages = {351--361},
     publisher = {mathdoc},
     volume = {46},
     number = {5},
     year = {2010},
     mrnumber = {2753989},
     zbl = {1249.34024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010__46_5_a5/}
}
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Medvedev, Alexandr. Geometry of third order ODE systems. Archivum mathematicum, Tome 46 (2010) no. 5, pp. 351-361. http://geodesic.mathdoc.fr/item/ARM_2010__46_5_a5/