Abstract
In any theoretical investigation of a real physical system, one is always forced to make simplifying assumptions concerning the true nature of the system. Since such idealizations are inevitable, it is reasonable to inquire as to how far one can go in this direction and still obtain satisfactory results. In certain cases, for example the motion of the planets, the equations of celestial mechanics provide a quite accurate model of the real physical system. In other situations, such as ecological or chemical interactions, or the study of large scale atmospheric phenomena, one either writes down certain reasonable relations between the quantities involved and their rates of change, or one tremendously reduces the number of actual equations involved. If such “leaps of faith” are to be of any use, it is necessary to study “rough” equations in “rough” terms. This in a nutshell, is our aim in this chapter and the next one. In other words, we want to fit these vague notions into a precise mathematical framework.
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© 1983 Springer-Verlag New York Inc.
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Smoller, J. (1983). The Conley Index. In: Shock Waves and Reaction—Diffusion Equations. Grundlehren der mathematischen Wissenschaften, vol 258. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0152-3_22
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DOI: https://doi.org/10.1007/978-1-4684-0152-3_22
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0154-7
Online ISBN: 978-1-4684-0152-3
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