Abstract
The main result of this Note is the following: for an algebraic system which evolution depends on variables which are partitionned into w and z, the elimination of the z leads to one set of differential algebraic equations (hence, with no inequations) if the projection map along z is a finite morphism of algebraic varieties; that is, if the differential algebra which defines the system is integral over a suitable differential subalgebra. To obtain this result, is lifted to differential algebra a more general, and well-known result in algebraic geometry which states that a finite morphism of algebraic varieties is a closed one with respect to the Zariski topology.
Key Words
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P.J. Cassidy: [1972] Differential algebraic groups, Amer. J. Math., 94, 891–954.
S. Diop: [1991] Elimination in control theory, Math. Control Signals Systems, 4, 17–32.
M. Fliess: [1989]: Automatique et corps différentiels, Forum Math., 1, 227–238.
R.E. Kolchin: [1973]: Differential Algebra and Algebraic Groups, Academic Press, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
This Note is dedicated to the memory of Wagaan Juuf.
Rights and permissions
Copyright information
© 1991 Birkhäuser Boston
About this chapter
Cite this chapter
Diop, S. (1991). Finite morphisms of differential algebraic varieties and elimination theory. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_16
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3214-8_16
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
eBook Packages: Springer Book Archive