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A.D. Bryuno (1979)
Lokal?nyi metod nelineinogo analiza differentsial?nykh uravnenii
ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 3, pp. 327–339. c Pleiades Publishing, Inc., 2006. Original Russian Text c V.V. Basov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 3, pp. 308–319. ORDINARY DIFFERENTIAL EQUATIONS A Generalized Normal Form and Formal Equivalence of Two-Dimensional Systems with Quadratic Zero Approximation: III V. V. Basov St. Petersburg State University, St. Petersburg, Russia Received June 16, 2003 DOI: 10.1134/S0012266106030037 The present paper continues [1, 2], and hence we retain the notation and continue the numbering of sections, formulas, theorems, remarks, corollaries, and examples. 2 2 9. SYSTEMS WITH ZERO APPROXIMATION (x ,x + x x ) 1 2 1 1 Consider system (1) whose unperturbed part belongs to the irregular case and can be reduced to the canonical form (23). We assume that system (1) is already represented in the form 2 2 x ˙ = x + X (x ,x ) , x ˙ = x + x x + X (x ,x ) , (115) 1 1 1 2 2 1 2 2 1 2 1 1 i.e., a ,a , 2b =1 and b ,c ,c = 0 in it. 1 2 2 1 1
Differential Equations – Springer Journals
Published: Apr 17, 2006
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