Lie Algebras, Structure of Nonlinear Systems and Chaotic Motion
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چکیده
We shall define a Lie algebra associated with this system to be the Lie subalgebra of g`(n, C) generated by all the matrices A(x), x ∈ R, and we shall denote it by LA. One of the main objectives of this paper is to demonstrate that the classical structure theory of this Lie algebra has important consequences for stability theory and chaotic motion. In fact, we shall see that the well-known chaotic systems of Lorentz and Chua [Matsumoto et al., 1985; Pivka et al., 1996; Khibnik, 1993] have a natural representation in terms of the Lie algebra LA and lead to an immediate extension to higherdimensional chaotic structures. Using the structure theory of Lie algebras (see [Sagle & Walde, 1973; Jacobson, 1962] and Sec. 2 of this paper), we can write the system in the form
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تاریخ انتشار 1998