论文信息 - LIE ALGEBRAS AND LINEAR DIFFERENTIAL EQUATIONS

LIE ALGEBRAS AND LINEAR DIFFERENTIAL EQUATIONS

Publisher Summary This chapter discusses certain symmetry properties possessed by the solutions of linear differential equations. The two results are established on the Lie algebra generated by a pair ofn by nmatrices. In order to avoid undue repetition, one agrees to call a matrix of rational functionsG(s) regular if it is square and approaches zero as|s| approached infinity. It is possible to associate a Lie algebra with each regular matrix of rational functions in a natural way. The symplectic matrices form a group and the Eigen values of symplectic matrices occur in reciprocal pairs. That is to say, if λ is an eigenvalue of a symplectic matrix. then so is 1/λ. This observation together with the basic ideas of Floquet theory enables one to show that for 0 ≤ t

Roger W. Brockett | R. Brockett | Abdolhossein Rahimi | A. Rahimi

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