Manuscript XIV-J@1 · XIV-J.tex · section · 1c0e72ca

One local chart in the unchanged common space

J2b: the supported response sector as finite normal jets › One local chart in the unchanged common space · lines 990–1025

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Define

S_{resp} = {q_{R} = 0, a = z} \subset W, K_{supp} := K_{6} + K_{8} + K_{9} .

This is the supported response sector, not the full six-branch kernel.

Work locally in a coordinate neighborhood $U \subset W$ of a retained point. The response incidence is regular there by the copied separated-endpoint geometry. Choose coordinates

(s, n) \in S_{0} \times B_{5}, n = (q_{R}, a^{0} - z^{0}, \dots, a^{3} - z^{3}), S_{resp} \cap U = {n = 0} .

Here $s$ has eleven components and includes the four independent $y$ coordinates.

All local distributions are represented relative to the chosen coordinate density. The smooth density conversion from the original flat variables is included in their coefficients.

The characteristic set remains

N_{U} = N \cap U .

It is a submanifold of $S_{resp}$ of relative codimension three, since $dim S_{resp} = 11$ and $dim N = 8$ .

Displayed formulas in this passage

unlabeled · line 993
$S_{resp} = {q_{R} = 0, a = z} \subset W, K_{supp} := K_{6} + K_{8} + K_{9} .$
unlabeled · line 1005
$(s, n) \in S_{0} \times B_{5}, n = (q_{R}, a^{0} - z^{0}, \dots, a^{3} - z^{3}), S_{resp} \cap U = {n = 0} .$
unlabeled · line 1020
$N_{U} = N \cap U .$

Nearby in this section

scope: The ambient problem is unchanged