Geodesic
Asymptotic Behavior of Solutions of Dynamic Equations
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 1, Tome 1 (2003), pp. 30-39.

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We consider linear dynamic systems on time scales, which contain as special cases linear differential systems, difference systems, or other dynamic systems. We give an asymptotic representation for a fundamental solution matrix that reduces the study of systems in the sense of asymptotic behavior to the study of scalar dynamic equations. In order to understand the asymptotic behavior of solutions of scalar linear dynamic equations on time scales, we also investigate the behavior of solutions of the simplest types of such scalar equations, which are natural generalizations of the usual exponential function. 
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S. Bodine; M. Bohner; D. Lutz. Asymptotic Behavior of Solutions of Dynamic Equations. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 1, Tome 1 (2003), pp. 30-39. http://geodesic.mathdoc.fr/item/CMFD_2003_1_a2/

[1] Benzaid Z., Lutz D. A., “Asymptotic representation of solutions of perturbed systems of linear difference equations”, Stud. Appl. Math., 77 (1987), 195–221 | MR | Zbl

[2] Bodine S., Lutz D. A., “Exponential functions on time scales: Their asymptotic behavior and calculation”, Dyn. Syst. Appl., 2002 | MR

[3] Bohner M., Lutz D. A., “Asymptotic behavior of dynamic equations on time scales”, J. Difference Equ. Appl., 7:1 (2001), 21–50, Special issue in memory of W. A. Harris, Jr. | DOI | MR | Zbl

[4] Bohner M., Peterson A., Dynamic equations on time scales: an introduction with applications, Birkhäuser Boston Inc., Boston, 2001 | MR | Zbl

[5] Bohner M., Peterson A., Advances in dynamic equations on time scales, Birkhäuser Boston Inc., Boston, 2002 | MR

[6] Eastham M. S. P., The asymptotic solution of linear differential systems. Applications of the Levinson theorem, Oxford University Press, Oxford, 1989 | MR | Zbl

[7] Harris W. A., Lutz D. A., “On the asymptotic integration of linear differential systems”, J. Math. Anal. Appl., 48:1 (1974), 1–16 | DOI | MR | Zbl

[8] Harris W. A., Lutz D. A., “Asymptotic integration of adiabatic oscillators”, J. Math. Anal. Appl., 51:1 (1975), 76–93 | DOI | MR | Zbl

[9] Harris W. A., Lutz D. A., “A unified theory of asymptotic integration”, J. Math. Anal. Appl., 57:3 (1977), 571–586 | DOI | MR | Zbl

[10] Hilger S., “Analysis on measure chains — a unified approach to continuous and discrete calculus”, Result. Math., 18 (1990), 19–56 | MR

[11] Levinson N., “The asymptotic nature of solutions of linear differential equations”, Duke Math. J., 15 (1948), 111–126 | DOI | MR | Zbl