Construction of minimal cocycles arising from specific differential equations
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.
scientific article; zbMATH DE number 1062367
scientific article