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Dynamical characterization of the Lyapunov form of matrices. (English) Zbl 1076.15013
The paper presents a dynamical characterization of the Lyapunov form for matrices, by looking at the induced flows on the projective space, the flag manifold and the Grassmannians.

15A21Canonical forms, reductions, classification
37B25Lyapunov functions and stability; attractors, repellers
Full Text: DOI
[1] Colonius, F.; Kliemann, W.: Morse decompositions and spectra on flag bundles. J. dynam. Differ. equ. 14, 719-741 (2002) · Zbl 1037.37009
[2] Colonius, F.; Kliemann, W.: The dynamics of control. (2000) · Zbl 1020.93500
[3] C. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series, no. 38, American Mathematical Society, 1978 · Zbl 0397.34056
[4] Hirsch, M.; Smale, S.: Differential equations, dynamical systems and linear algebra. (1974) · Zbl 0309.34001
[5] Palis, J.; De Melo, W.: Geometric theory of dynamical systems. (1982) · Zbl 0491.58001
[6] Warner, F.: Foundations of differentiable manifolds and Lie groups. (1983) · Zbl 0516.58001
[7] Wiggins, S.: Introduction to applied nonlinear dynamical systems and applications. (1996) · Zbl 0870.70019
[8] Arrowsmith, D. K.; Place, C. M.: An introduction to dynamical systems. (1990) · Zbl 0702.58002