Point classification of 2nd order ODEs:Tresse classification revisited and beyond

By B. Kruglikov. 2008

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In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the second order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification and also discuss the role of absolute invariants and the equivalence problem.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4a6203eae9a70e7fcf2431fc4ee335a6c5b9570e