Contact transformations and local reducibility of ODE to the form $y"'=0$

Abstract: Contact group orbits of the ODE $y"'=0$ in corresponding jet bundles are investigated. Explicit relations for the right-hand side of an arbitrary 3-order ODE necessary and sufficient for the existence of a contact transformation reducing this equation locally to the form $y"'=0$ are obtained.

Keywords: Ordinary differential equation, jet bundle, contact transformation, equivalence problem, linearizability.

Classification (MSC91): 34A26, 53A55, 34A30, 34C20, 58F35

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