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Reduction of systems of linear differential equations to Jordan normal form. (English) Zbl 0166.03703


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[1] SeeCoddington andLevinson,Theory of Ordinary Differential Equations (1955), Chapter 3,G. Sansone andR. Conti,Equazioni Differenziali Non Lineari (Rome 1956), Chapter VIII,V. V. Nemitsky andV. V. Stepanof,Qualitative theory of differential equations, 2nd ed. Moscow 1949.
[2] SeeSansone andConti, p. 543 footnote 11.
[3] E. Coddington andLevinson, Perturbations of linear systems with constaut coefficients possessing periodic solutions,Contributions to the theory of non-linear oscillations, Vol 2, edS. Lefschetz, « Annals of Maths Studies », 29, 1952, 19-35,H. L. Turritin, Asymptotic expansions of solutions of systems of ordinary differential equations containing a parameter,loc. cit, 81-116,P. Mendelson, On phase portraits of critic 1 points in -space,Contributions to the theory of non-linear oscillations, Vol. 4, edS. Lefschetz, « Annals of Maths Studies », 41 (1958), 167-199,D. Bushaw,Differential equations with a discontinuous forcing term, Experimental Towing Tank, Stevens Institute of Technology No. 469 (1953),Z. Szmydt, On th degree of regularity of surfaces formed by the asymptotic integrals of differential equations, « Annales Polonici Mathematici », II 2 (1955), 294-313.
[4] SeeJ. A. Todd,Projective and analytical geometry, (London 1947), 166. · Zbl 0031.06701
[5] The two following sections are based onO. Schreier andE. Sperner,Introduction to Modern Algebra and Matrix Theory, translated byM Davis andM. Hausner, (New York 1951) 344-371 where further details of the algebraic processes will be found.
[6] SeeJ. A. Todd, loc. cit. 152-4.
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