# Jet

From Encyclopedia of Mathematics

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.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Jet&oldid=17431

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article