Geodesic
Method of local construction of invariant subspaces in the solution space of Chew–Low equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 1, pp. 78-93 
V. A. Meshcheryakov; K. V. Rerikh. Method of local construction of invariant subspaces in the solution space of Chew–Low equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 1, pp. 78-93. http://geodesic.mathdoc.fr/item/TMF_1970_3_1_a5/
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     title = {Method of local construction of invariant subspaces in the solution space of {Chew{\textendash}Low} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A nonlinear system offunctlonal equations for the matrix elements of the $S$-matrix is formulated on the basis of Chew–Low equations. A transition is made to projective coordinates in the spade of the matrix elements of the $S$-matrix and the unitarity condiflons are linearlzed. On the basis of a geometrical interpretation of the system of nonlinear functional equations as a transformation in an $(n-1)$-dimensional real space, it is shown that some of the solutions of the original system of equations lie on invariant hypersurfaecs of this space. A method is proposed for the local construction of the invariant hypersurfaces in the neighborhood of the fixed points of the transformation. This method is applied to the Chew–Low equations with $3\times 3$ and $4\times 4$ crossing matrices. It is shown that, if the Chew–Low equations have a selution, the arbitrariness, which is a generalization of the well-known $\beta$-arbitrariness, in the solutions of the class considered is not exhaustive.

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