Local invariants of differential equations |
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Authors: | A D Bryuno |
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Institution: | (1) Institute of Applied Mathematics, Academy of Sciences of the USSR, USSR |
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Abstract: | We consider an analytic system X= (X) in the neighborhood of the fixed point X=0. Depending on the characteristic numbers of the matrix (![part](/content/v3656278414kk65j/xxlarge8706.gif) / x)0, we define the integer d 0 as the dimension of the normal form or as the multiplicity of the resonance. We show that a system with d=1, subject to certain additional assumptions, has a finite number of invariants relative to reversible formal changes of variablesx = (Y). All these invariants are the coefficients of some normal form. We touch upon questions concerning invariants of relatively smooth and continuous substitutions.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 499–507, October, 1973. |
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