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Lyapunov Direction Fields

机译：李亚普诺夫方向场

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Linearization around the chaotic orbits of dynamical systems offers good prospects for understanding complex systems. The naturally available information that can be obtained from such studies are the magnitudes and directions in phase space of stretching and shrinking of an initial small sphere or realizations. In this note we give an algebraic foundation to the geometric methods that have been previously used to study this. The equations of evolution of the orthogonal principal stretching and contraction directions show that asymptotically they depend only on the location in phase space, and not on the orbit. As an example, we show that these directions sketch out the attractor of the Lorenz model. (ERA citation 11:042096)

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