Geodesic
Solution manifolds for systems of differential equations
Theory and applications of categories, Tome 7 (2000), pp. 239-262 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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This paper defines a solution manifold and a stable submanifold for a system of differential equations. Although we eventually work in the smooth topos, the first two sections do not mention topos theory and should be of interest to non-topos theorists. The paper characterizes solutions in terms of barriers to growth and defines solutions in what are called filter rings (characterized as $C^{\infty}$-reduced rings in a paper of Moerdijk and Reyes). We examine standardization, stabilization, perturbation, change of variables, non-standard solutions, strange attractors and cycles at infinity.

Classification : 18B25, 58F14, 26E35.
Keywords: smooth topos, differential equation. 
@article{TAC_2000_7_a12,
     author = {John F. Kennison},
     title = {Solution manifolds for systems of differential equations},
     journal = {Theory and applications of categories},
     pages = {239--262},
     year = {2000},
     volume = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2000_7_a12/}
}
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John F. Kennison. Solution manifolds for systems of differential equations. Theory and applications of categories, Tome 7 (2000), pp. 239-262. http://geodesic.mathdoc.fr/item/TAC_2000_7_a12/