Abstract
It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) − x of complexity two, (4) d = 0 in all remaining cases.
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References
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The research was financially supported by the Russian Foundation for Basic Research (grant no. 17-01-00592 a).
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Beloshapka, V.K. Stabilizer of a function in the gage group. Russ. J. Math. Phys. 24, 148–152 (2017). https://doi.org/10.1134/S1061920817020029
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DOI: https://doi.org/10.1134/S1061920817020029