Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bougerol, P., and J. Lacroix: Products of random matrices with applications to Schrödinger operators. Boston-Basel-Stuttgart: Birkhäuser (in press).
Bylov, B. F., R. E. Vinograd, D. M. Grobman, and V. V. Nemyckiǐ: Theory of Lyapunov exponents. Moscow: Nauka 1966 (in Russian).
Carmona, R.: Random Schrödinger operators. Lecture Notes, Ecole d'Été de Probabilités de Saint-Flour XIV-1984 (to appear).
Carverhill, A.: Flows of stochastic dynamical systems: ergodic theory. Stochastics 14 (1985), 273–317.
Coddington, E. A., and Levinson, N.: Theory of ordinary differential equations. New York: McGraw-Hill 1955.
Crauel, H.: PhD thesis. Bremen 1985
Delyon, F., Levy, Y. and B. Souillard: Andersen localization for multidimensional systems at large disorder or low energy. Comm. Math. Phys. (to appear).
Doob, J.: Stochastic processes. New York: Wiley 1953.
Duong, H. H.: Theory of characteristic vectors and its application to study the stability of solutions of differential equations. Report No. 139 Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, 1985.
Eckmann, J.-P., and D. Ruelle: Ergodic theory of chaos and strange attractors. Preprint IHES/P/85/15.
Furstenberg, H., and H. Kesten: Products of random matrices. Annals Math. Statist. 31 (1960), 457–469.
Furstenberg, H.: Noncommuting random products. Trans. Amer. Math. Soc. 108 (1963), 377–428.
Furstenberg, H.: A Poisson formula for semi-simple Lie groups. Ann. of Math. 77 (1963), 335–386.
Gol'dsheid, I. J., S. A. Molčanov, and L. A. Pastur: A random one-dimensional Schrödinger operator has a pure point spectrum. Functional Anal. Appl. 11 (1977), 1–10.
Guivarc'h, Y., and A. Raugi: Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence. Z. Wahrscheinlichkeitstheorie verw. Gebiete 69 (1985), 187–242.
Guivarc'h, Y., and A. Raugi: Products of random matrices. Convergence theorems. Preprint 1985.
Has'minskiǐ, R. Z.: Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems. Theory Probability Appl. 12 (1967), 144–147.
Has'minskiǐ, R. Z.: Stochastic stability of differential equations. Alphen: Sijthoff and Noordhoff 1980 (translation of the Russian edition, Moscow; Nauka 1969).
Hoan, N. T.: On uniform stability of the characteristic spectrum for sequences of systems of linear differential equations. Report No. 139, Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, 1985.
Kifer, Y.: Ergodic theory of random transformations. Boston-Basel-Stuttgart: Birkhäuser 1985.
Kotani, S.: Lyapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrödinger operators. In: K. Itō (ed.): Stochastic Analysis, Proceedings of the Taniguchi International Symposium, Katata and Kyoto, 1982, 225–247. Amsterdam-New York-Oxford: North-Holland 1984.
Kozin, F.: Stability of linear stochastic systems. In: R. Curtain (ed.): Stability of stochastic dynamical systems. Lecture Notes in Mathematics, No. 294, 186–229. Berlin-Heidelberg-New York: Springer 1972.
Kunita, H.: Stochastic differential equations and stochastic flows of diffeomorphisms. École d'Été de Probabilités de Saint-Flour XII-1982. Lecture Notes in Mathematics, No. 1097, 143–303. Berlin-Heidelberg-New York-Tokyo: Springer 1984.
Ledrappier, F.: Quelques propriétés des éxposants caracteristiques. École d'Été de Probabilités de Saint-Flour XII-1982. Lecture Notes in Mathematics, No. 1097, 305–396. Berlin-Heidelberg-New York-Tokyo: Springer 1984.
Lyapunov, A. M.: Problème générale de la stabilité du mouvement. Comm. Soc. Math. Kharkov 2 (1892), 3 (1983), 265–272. Ann. Fac. Sci. Toulouse 9 (1907), 204–474. Reprint: Ann. of Math. Studies 17. Princeton: Princeton University Press 1949.
Millionščikov, V. M.: On the spectral theory of nonautonomous linear systems of differential equations. Trans. Moscow Math. Soc. 18 (1968), 161–206.
Molčanov, S. A.: The structure of eigenfunctions of one-dimensional unordered structures. Math. USSR Izvestija 12 (1978), 69–101.
Oseledec, V. I.: A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 (1968), 197–231.
Papanicolaou, G., and J. B. Keller: Stochastic differential equations with applications to random harmonic oscillators and wave propagation in random media. SIAM J. Appl. Math. 21 (1971), 287–305.
Pesin, Y. B.: Lyapunov characteristic exponents and smooth ergodic theory. Russian Math. Survey 32 (1977), 55–114.
San Martin, L., and L. Arnold: A control problem on the projective bundle, with applications to the Lyapunov spectrum of stochastic flows. Matemática Aplicada e Computacional (to appear).
Tutubalin, V. N.: On limit theorems for a product of random matrices. Theory Probability Appl. 10 (1965), 25–27.
Virtser, A. D.: On the simplicity of the spectrum of the Lyapunov characteristic indices of a product of random matrices. Theory Probability Appl. 28 (1983), 122–135.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Arnold, L., Wihstutz, V. (1986). Lyapunov exponents: A survey. In: Arnold, L., Wihstutz, V. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076830
Download citation
DOI: https://doi.org/10.1007/BFb0076830
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16458-6
Online ISBN: 978-3-540-39795-3
eBook Packages: Springer Book Archive