Lyapunov and Sacker-Sell spectral intervals

Journal of Dynamics and Differential Equations

Volumn 19, Issue 2, 2007, Pages 265-293

  Dieci, Luca ^a   Van Vleck, Erik S ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF KANSAS   (United States)

Author keywords

Exponential dichotomy; Integral separation; Lyapunov exponents; Sacker Sell spectrum

Indexed keywords

EID: 34249880487     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-006-9030-5     Document Type: Article

References (24)

1. Adrianova, L. Ya. (1980). Introduction to Linear Systems of Differential Equations, Translations of Mathematical Monographs, Vol. 146, AMS, Providence, RI.
2. Benettin, G., Galgani, L., Giorgilli, A. and Strelcyn, J.-M. Lyapunov exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: theory ", and "... Part 2: numerical applications. Meccanica 15, 9-20, 21-30.
3. Bylov, B. F. (1965). On the reduction of systems of linear equations to the diagonal form. Math. Sb. 67, 338-334.
4. Bylov, B. F., and Izobov, N. A. (1969). Necessary and sufficient conditions for stability of characteristic exponents of a linear system. Differentsial'nye Uravneniya 5, 1794-1903.
5. Bylov, B. F., Vinograd, R. E., Grobman, D. M., and Nemyckii, V. V. (1966). The theory of Lyapunov exponents and its applications to problems of stability. Nauka Publishers, Moscow.
6. Coppel, W A. (1978). Dichotomies in Stability Theory. Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin.
7. Dieci, L., and Van Vleck, E. S. (2002). Lyapunov and other spectra: a survey. In D. Estep and S. Tavener (eds), Preservation of Stability under Discretization. SIAM Publications, Pliladelphia, pp.
8. Dieci, L., and Van Vleck, E. S. (2003). Lyapunov spectral intervals: theory and computation. SIAM J. Numer. Anal. 40, 516-542.
9. Dieci, L., and Van Vleck, E. S. (2005). On the error in computing Lyapunov exponents by QR methods. Numer. Math. 101, 619-642.
10. Dieci, L., and Van Vleck, E. S. (2006). Perturbation theory for the approximation of Lyapunov exponents by QR methods. J. Dyn. Diff. Eq. DOI: 10.1007/s10884-006-9024-3
11. Diliberto, S. P. (1950). On Systems of Ordinary Differential Equations. In Contributions to the Theory of Nonlinear Oscillations (Ann. of Math. Studies 20), Princeton University Press, Princeton, pp. 1-38.
12. Johnson, R. A. (1987). The Oseledec and Sacker-Sell spectra for almost periodic linear systems: an example, P. Amer. Math. Soc. 99, 261-267.
13. Lillo, J. C. (1960). Perturbations of nonlinear systems, Acta Math. 103, 123-138.
14. Lillo, J. C. (1960). A note on the continuity of characteristic exponents. Proc. Nat. Acad. Sci. 46, 247-250.
15. Lyapunov, A. (1992). Problém géneral de la stabilité du mouvement. Int. J. Control 53, 531-773.
16. Millionshchikov, V. M. (1969). Structurally stable properties of linear systems of differential equations. Differentsial'nye Uravneniya 5, 1775-1784.
17. Millionshchikov, V. M. (1968). Proof of the existence of non-irreducible systems of linear differential equations with almost periodic coefficient. Diff. Eq. 4, 203-205.
18. Oseledec, V. I. (1968). A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19, 197.
19. Palmer, K. J. (1982). Exponential dichotomy, integral separation and diagonalizability of linear systems of ordinary differential equations. J. Diff. Eq. 43, 184-203.
20. Palmer, K. J. (1982). Exponential separation, exponential dichotomy and spectral theory for linear systems of ordinary differential equations. J. Diff. Eq. 46, 324-345.
21. Palmer, K. J. (2000). Shadowing in Dynamical Systems: Theory and Applications. Mathematics and its applications, Vol. 501, Kluwer Academic Publishers, Dordrecht-Boston.
22. Perron, O. (1930). Die Ordnungszahlen Linearer Differentialgleichungssysteme. Math. Zeits. 31, 748-766.
23. Pilyugin, S. Yu. (1999). Shadowing in Dynamical Systems. Lecture Notes in Math, Vol. 1706, Springer-Verlag, Berlin-Heidelberg.
24. Sacker, R. J., and Seil, G. R. (1978). A spectral theory for linear differential systems. J. Diff. Eq. 7, 320-358.