The Oseledec and Sacker-Sell spectra for almost periodic linear systems: an example
HTML articles powered by AMS MathViewer
- by Russell A. Johnson
- Proc. Amer. Math. Soc. 99 (1987), 261-267
- DOI: https://doi.org/10.1090/S0002-9939-1987-0870782-7
- PDF | Request permission
Abstract:
We give an example illustrating the relation between the Oseledec spectrum (roughly speaking, the set of Lyapunov exponents) and the Sacker-Sell (or continuous) spectrum for Bohr almost periodic linear systems.References
- A. Coppel, Dichotomies and stabilitity theory, Lecture Notes in Math., vol. 629, Springer-Verlag, Berlin and New York, 1978.
- Ju. L. Dalec′kiĭ and M. G. Kreĭn, Stability of solutions of differential equations in Banach space, Translations of Mathematical Monographs, Vol. 43, American Mathematical Society, Providence, R.I., 1974. Translated from the Russian by S. Smith. MR 0352639
- Robert Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York, 1969. MR 0267561
- Robert Ellis and Russell A. Johnson, Topological dynamics and linear differential systems, J. Differential Equations 44 (1982), no. 1, 21–39. MR 651685, DOI 10.1016/0022-0396(82)90023-7
- Harry Furstenberg, Harvey Keynes, and Leonard Shapiro, Prime flows in topological dynamics, Israel J. Math. 14 (1973), 26–38. MR 321055, DOI 10.1007/BF02761532
- Russell A. Johnson, The recurrent Hill’s equation, J. Differential Equations 46 (1982), no. 2, 165–193. MR 675906, DOI 10.1016/0022-0396(82)90114-0 R. Johnson, K. Palmer and G. Sell, Ergodic theory of linear dynamical systems, SIAM J. Appl. Math. (to appear). V. Millionshchikov, Metric theory of linear systems of differential equations, Math. USSR-Sb. 6 (1968), 149-158. —, Proof of the existence of non-irreducible systems of linear differential equations with almost periodic coefficients, J. Differential Equations 4 (1968), 203-205.
- V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210 (Russian). MR 0240280 L. Pontryagin, Topologische Gruppen, Deutsche Ubersetzung, Teubner Verlag, Leipzig, 1957.
- Robert J. Sacker and George R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. I, J. Differential Equations 15 (1974), 429–458. MR 341458, DOI 10.1016/0022-0396(74)90067-9
- Robert J. Sacker and George R. Sell, A spectral theory for linear differential systems, J. Differential Equations 27 (1978), no. 3, 320–358. MR 501182, DOI 10.1016/0022-0396(78)90057-8
- W. A. Veech, Almost automorphic functions on groups, Amer. J. Math. 87 (1965), 719–751. MR 187014, DOI 10.2307/2373071
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 261-267
- MSC: Primary 34C35; Secondary 54H20, 58F19, 58F27
- DOI: https://doi.org/10.1090/S0002-9939-1987-0870782-7
- MathSciNet review: 870782