Abstract
A definite theory exists for solving linear systems of ordinary differential equations with constant coefficients. “This theory is essentially a branch of linear algebra, and allows us to solve all autonomous linear equations”, ([4], p. 95). Furthermore, “In view of the fact that the solution of these equations does not, in principle, present any great difficulties, they are often considered to be of no great interest for theory, and in textbooks they are usually relegated to the position of simple exercises appended to the general theory of linear equations”, ([81], p. 41). Modern textbooks [8, 21, 26, 44, 45, 46, 50, 90] give a detailed and rigorous treatment of the standard methods available for linear problems, supplemented with numerous mechanical, electrical, and engineering applications. The voluminous literature accumulated on the general properties of the solutions of linear differential equations must therefore no doubt leave the impression that no further contribution could be made to the standard normal linear dynamic system with real and constant coefficients. This impression, however, will fade rather quickly as we go on. Paradoxically, some fundamental aspects of this simple dynamic system are still unnoticed.
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© 1994 Springer Science+Business Media Dordrecht
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Jensen, B.S. (1994). Linear and Affine Dynamics in the Plane. In: The Dynamic Systems of Basic Economic Growth Models. Mathematics and Its Applications, vol 302. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1036-5_15
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DOI: https://doi.org/10.1007/978-94-011-1036-5_15
Publisher Name: Springer, Dordrecht
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