de Anda, Miguel Ángel Gutiérrez On the calculation of Lyapunov characteristic exponents for continuous-time LTV dynamical systems using dynamic eigenvalues. (English) Zbl 1270.34156 Int. J. Bifurcation Chaos Appl. Sci. Eng. 22, No. 1, Article ID 1250019, 10 p. (2012). Summary: The concept of the dynamic eigenvalues may be used, in principle, to formulate in a general way analytic solutions of continuous-time linear time-varying dynamical (LTV) systems. It has also been suggested that the mean value of these quantities may be used to calculate Lyapunov characteristic exponents for the aforementioned systems. In this article, it will be demonstrated that this conjecture is not necessarily valid. Cited in 1 Document MSC: 34D08 Characteristic and Lyapunov exponents of ordinary differential equations 34A30 Linear ordinary differential equations and systems Keywords:linear time-varying systems; dynamic eigenvalues; Lyapunov characteristic exponents PDFBibTeX XMLCite \textit{M. Á. G. de Anda}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 22, No. 1, Article ID 1250019, 10 p. (2012; Zbl 1270.34156) Full Text: DOI References: [1] Adrianova L., Introduction to Linear Systems of Differential Equations (1995) · Zbl 0844.34001 [2] DOI: 10.4064/fm206-0-2 · Zbl 1187.37036 · doi:10.4064/fm206-0-2 [3] DOI: 10.1109/TAC.1972.1099875 · Zbl 0259.93029 · doi:10.1109/TAC.1972.1099875 [4] DOI: 10.1007/BF02128236 · Zbl 0488.70015 · doi:10.1007/BF02128236 [5] DOI: 10.1007/BF02128237 · doi:10.1007/BF02128237 [6] DOI: 10.1088/0951-7715/10/5/004 · Zbl 0910.34055 · doi:10.1088/0951-7715/10/5/004 [7] DOI: 10.1137/S0036142901392304 · Zbl 1021.65067 · doi:10.1137/S0036142901392304 [8] DOI: 10.1007/BF03322513 · Zbl 0964.34005 · doi:10.1007/BF03322513 [9] DOI: 10.1016/0167-2789(84)90282-3 · Zbl 0588.58036 · doi:10.1016/0167-2789(84)90282-3 [10] DOI: 10.1103/PhysRevLett.74.70 · doi:10.1103/PhysRevLett.74.70 [11] DOI: 10.1142/S0218127405014519 · Zbl 1094.34526 · doi:10.1142/S0218127405014519 [12] DOI: 10.1016/0022-0396(70)90005-7 · Zbl 0202.09302 · doi:10.1016/0022-0396(70)90005-7 [13] DOI: 10.1016/j.jsv.2006.06.035 · Zbl 1243.74200 · doi:10.1016/j.jsv.2006.06.035 [14] DOI: 10.1007/BF01138331 · Zbl 0622.34038 · doi:10.1007/BF01138331 [15] DOI: 10.1063/1.1741751 · Zbl 1080.37032 · doi:10.1063/1.1741751 [16] DOI: 10.1063/1.1768911 · Zbl 1080.34038 · doi:10.1063/1.1768911 [17] DOI: 10.1063/1.3314277 · Zbl 1311.34016 · doi:10.1063/1.3314277 [18] DOI: 10.1007/s10884-009-9128-7 · Zbl 1165.65050 · doi:10.1007/s10884-009-9128-7 [19] DOI: 10.1137/1.9780898719512 · doi:10.1137/1.9780898719512 [20] Millionščikov V., Diff. Eqns. 4 pp 203– [21] Millionščikov V., Diff. Eqns. 5 pp 1475– [22] DOI: 10.1016/0960-0779(94)00170-U · Zbl 1080.34540 · doi:10.1016/0960-0779(94)00170-U [23] Polyanin A., Handbook of Exact Solutions for Ordinary Differential Equations (2003) · Zbl 1015.34001 [24] DOI: 10.1103/PhysRevLett.80.3747 · doi:10.1103/PhysRevLett.80.3747 [25] DOI: 10.1007/978-3-642-04458-8_2 · doi:10.1007/978-3-642-04458-8_2 [26] DOI: 10.1103/PhysRevE.82.036704 · doi:10.1103/PhysRevE.82.036704 [27] DOI: 10.1142/S021812740701955X · Zbl 1146.34321 · doi:10.1142/S021812740701955X [28] DOI: 10.1007/978-94-015-8921-5 · doi:10.1007/978-94-015-8921-5 [29] Vinograd R., Diff. Eqns. 11 pp 474– [30] DOI: 10.1016/0167-2789(85)90011-9 · Zbl 0585.58037 · doi:10.1016/0167-2789(85)90011-9 [31] DOI: 10.1016/0024-3795(91)90235-O · Zbl 0719.15004 · doi:10.1016/0024-3795(91)90235-O This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.