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

Mathematics – Classical Analysis and ODEs

Scientific paper

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Scientific paper

In 1896 Tresse gave a complete description of relative differential
invariants for the pseudogroup action of point transformations on the 2nd 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.

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