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Attainable sets and one-parameter semigroups of sets

Published online by Cambridge University Press:  18 May 2009

I. Chon  and
J. D. Lawson
I. Chon
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA Electronic address MMLAWS@LSUVAX
J. D. Lawson
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA Electronic address MMLAWS@LSUVAX
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The methods of Lie theory have found widespread application in the study of the Lie algebras of vector fields on manifolds that arise naturally in geometric control theory (for some such applications, see [1]). Control systems on Lie groups themselves also have received considerable attention (see, for example, [9]). After reviewing basic facts about control systems on Lie groups, we derive the close relationship between attainable sets and Rådström's theory [12] of one-parameter semigroups of sets (Section 2). These ideas are then linked to the recently emerging Lie theory of semigroups [5]. The authors are indebted to the referee for pointing out some of the pertinent literature and analogous results from the area of geometric control.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 2 , May 1991 , pp. 187 - 201
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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