# Ordinary differential equations and their exponentials

Open Mathematics (2006)

- Volume: 4, Issue: 1, page 64-81
- ISSN: 2391-5455

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topAnders Kock, and Gonzalo Reyes. "Ordinary differential equations and their exponentials." Open Mathematics 4.1 (2006): 64-81. <http://eudml.org/doc/268742>.

@article{AndersKock2006,

abstract = {In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.},

author = {Anders Kock, Gonzalo Reyes},

journal = {Open Mathematics},

keywords = {34A99; 51K10; 18B25},

language = {eng},

number = {1},

pages = {64-81},

title = {Ordinary differential equations and their exponentials},

url = {http://eudml.org/doc/268742},

volume = {4},

year = {2006},

}

TY - JOUR

AU - Anders Kock

AU - Gonzalo Reyes

TI - Ordinary differential equations and their exponentials

JO - Open Mathematics

PY - 2006

VL - 4

IS - 1

SP - 64

EP - 81

AB - In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.

LA - eng

KW - 34A99; 51K10; 18B25

UR - http://eudml.org/doc/268742

ER -

## References

top- [1] M. Bunge and E. Dubuc: “Local Concepts in Synthetic Differential Geometry and Germ Representability”, In: D.W. Kueker, E.G.K. Lopez-Escobar and C.H. Smith (Eds.): Mathematical Logic and Theoretical Computer Science, Marcel Dekker Inc., 1987, pp. 93–159. Zbl0658.18004
- [2] C. Godbillon: Géométrie Différentielle et Mécanique Analytique, Hermann, Paris, 1969.
- [3] A. Kock: Synthetic Differential Geometry, Cambridge University Press, 1981.
- [4] A. Kock and G.E. Reyes: “Aspects of Fractional Exponents”, Theor. Appl. Categories, Vol. 5(10), (1999). Zbl0929.18002
- [5] A. Kock and G.E. Reyes: “Some calculus with extensive quantities; wave equation”, Theor. Appl. Categories, Vol. 11(14), (2003). Zbl1032.18005
- [6] A. Kumpera and D. Spencer: Lie equations, Vol. 1, Ann. of Math Studies, Vol. 73, Princeton University Press, 1972. Zbl0258.58015
- [7] R. Lavendhomme: Basic Concepts Of Synthetic Differential Geometry, Kluwer Academic Publishers, 1996. Zbl0866.58001
- [8] F.W. Lawvere: “Categorical Dynamics”, In: A. Kock (Ed.): Topos Theoretic Methods in Geometry, Series 30, Aarhus Various Publ., (1979).
- [9] B. Malgrange: “Equations de Lie”, I. J. Diff. Geom., Vol. 6, (1972), pp. 503–522.
- [10] I. Moerdijk and G.E. Reyes: Models for Smooth Infinitesimal Analysis, Springer-Verlag, 1991.

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