Construction of minimal cocycles arising from specific differential equations
type: Item
instance of: scholarly article
title: Construction of minimal cocycles arising from specific differential equations
zbMATH Open document ID: 0894.93004
DOI: 10.1007/BF02773645
author: Mahesh Nerurkar
author: Héctor J. Sussmann
published in: Israel Journal of Mathematics
publication date: 1998-08-10T00:00:00Z
review text: The authors combine methods from dynamical systems and control theory to develop a new technique to construct cocycles with desired dynamical properties. These cocycles arise as fundamental matrix solutions of linear differential equations evolving on connected and compact Lie groups \(G\), having coefficients that belong to a closed and convex subset \(S\) of the Lie algebra of \(G\). The dimension of \(S\) is allowed to be much smaller than the dimension of \(G\). This applies to a number of differential equations arising in Mathematical Physics. In particular, the ``Rabi oscillator'' is a system governed by an equation fitting in the general situation studied in this article.
Mathematics Subject Classification ID: 93B03
zbMATH DE Number: 1062367
zbMATH Keywords: accessibility
zbMATH Keywords: right-invariant control system
zbMATH Keywords: cocycles
zbMATH Keywords: Lie groups
zbMATH Keywords: Lie algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1062367