Difference between revisions of "Jet"
From Encyclopedia of Mathematics
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| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> | + | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> P. Bröcker, L. Lander, "Differentiable germs and catastrophes" , Cambridge Univ. Press (1975) {{MR|0494220}} {{ZBL|0302.58006}} </TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> W. Guillemin, "Stable mappings and their singularities" , Springer (1973) {{MR|0341518}} {{ZBL|0294.58004}} </TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> T. Poston, I. Stewart, "Catastrophe theory and its applications" , Pitman (1978) {{MR|0501079}} {{ZBL|0382.58006}} </TD></TR></table> |
Revision as of 16:58, 15 April 2012
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 |
How to Cite This Entry:
Jet. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Jet&oldid=24482
Jet. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Jet&oldid=24482
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article