Jet

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) MR0494220 Zbl 0302.58006
[2]	W. Guillemin, "Stable mappings and their singularities" , Springer (1973) MR0341518 Zbl 0294.58004
[3]	T. Poston, I. Stewart, "Catastrophe theory and its applications" , Pitman (1978) MR0501079 Zbl 0382.58006