Ordinary differential equations and their exponentials

• Autorzy: Anders Kock , Gonzalo Reyes
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Synthetic Differential Geometry; vector field; action; exponential object; 34A99; 51K10; 18B25

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 1
• Strony: 64-81

Daty

wydano

2006-03-01

online

2006-03-01

Twórcy

autor

Anders Kock

• University of Aarhus

autor

Gonzalo Reyes

• Université de Montréal

Bibliografia

• [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.
• [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).
• [5] A. Kock and G.E. Reyes: “Some calculus with extensive quantities; wave equation”, Theor. Appl. Categories, Vol. 11(14), (2003).
• [6] A. Kumpera and D. Spencer: Lie equations, Vol. 1, Ann. of Math Studies, Vol. 73, Princeton University Press, 1972.
• [7] R. Lavendhomme: Basic Concepts Of Synthetic Differential Geometry, Kluwer Academic Publishers, 1996.
• [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.

Identyfikatory

DOI

10.1007/s11533-005-0005-2