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:
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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
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