Construction of minimal cocycles arising from specific differential equations

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Blending methods of Topological Dynamics and Control Theory, we develop a new technique to construct compact-Lie-group-valued minimal cocycles arising as fundamental matrix solutions of linear differential equations with recurrent coefficients subject to a given constraint. The precise requirement on the coefficients is that they belong to a specified closed convex subset S of the Lie algebra L of the Lie group. Our result is proved for a very thin class of cocycles, since the dimension of S is allowed to be much smaller than that of L, and the only assumption on S is that L0(S) = L, where L0(S) is the ideal of L(S) generated by the difference set S - S, and L(S) is the Lie subalgebra of L generated by S. This covers a number of differential equations arising in Mathematical Physics, and applies in particular to the widely studied example of the Rabi oscillator.

Original languageEnglish (US)
Pages (from-to)309-326
Number of pages18
JournalIsrael Journal of Mathematics
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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