Geodesic
Solution manifolds for systems of differential equations
Theory and applications of categories, Tome 7 (2000), pp. 239-262.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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},
     publisher = {mathdoc},
     volume = {7},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2000_7_a12/}
}
TY  - JOUR
AU  - John F. Kennison
TI  - Solution manifolds for systems of differential equations
JO  - Theory and applications of categories
PY  - 2000
SP  - 239
EP  - 262
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2000_7_a12/
LA  - en
ID  - TAC_2000_7_a12
ER  - 
%0 Journal Article
%A John F. Kennison
%T Solution manifolds for systems of differential equations
%J Theory and applications of categories
%D 2000
%P 239-262
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2000_7_a12/
%G en
%F TAC_2000_7_a12
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/