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A polynomial obtained by the truncation of the (formal) Taylor series of a differentiable function . More precisely, let and be -manifolds. The class of equivalent triples , where is open, , is a mapping of class , is then called a -jet from to . Equivalence is defined thus:

if and if the local images of the mappings , at in relation to a pair of charts have identical derivatives up to the order , inclusive. The space of jets is a -manifold.


[1] P. Bröcker, L. Lander, "Differentiable germs and catastrophes" , Cambridge Univ. Press (1975)
[2] W. Guillemin, "Stable mappings and their singularities" , Springer (1973)
[3] T. Poston, I. Stewart, "Catastrophe theory and its applications" , Pitman (1978)
How to Cite This Entry:
Jet. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article