Point equivalence of second-order ODEs: Maximal invariant classification order. (March 2015)

• Record Type: Journal Article
• Authors: Milson, Robert; Valiquette, Francis
• Is Part Of: Journal of symbolic computation. Volume 67(2015)
• Page Start: 16
• Page End: 41
• Publication Date: 2015-03
• Subjects: 53A55; Differential invariants -- Moving frames -- Painlevé equations -- Point transformations -- Second-order ordinary differential equations; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2014.08.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We show that the local equivalence problem of second-order ordinary differential equations under point transformations is completely characterized by differential invariants of order at most 10 and that this upper bound is sharp. We also demonstrate that, modulo Cartan duality and point transformations, the Painlevé-I equation can be characterized as the simplest second-order ordinary differential equation belonging to the class of equations requiring 10th order jets for their classification.