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Journal of Modern Dynamics (JMD)
 

A concise proof of the multiplicative ergodic theorem on Banach spaces
Pages: 237 - 255, Volume 9, 2015

doi:10.3934/jmd.2015.9.237      Abstract        References        Full text (259.6K)           Related Articles

Cecilia González-Tokman - School of Mathematics and Physics, The University of Queensland, St Lucia QLD 4072, Australia (email)
Anthony Quas - Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, B.C., V8W 3R4, Canada (email)

1 A. Blumenthal, A volume-based approach to the multiplicative ergodic theorem on Banach spaces, arXiv:1502.06554.
2 T. S. Doan, Lyapunov Exponents for Random Dynamical Systems, PhD thesis, Fakultät Mathematik und Naturwissenschaften der Technischen Universität Dresden, 2009.
3 G. Froyland, S. Lloyd and A. Quas, Coherent structures and isolated spectrum for Perron-Frobenius cocycles, Ergodic Theory Dynam. Systems, 30 (2010), 729-756.       
4 C. González-Tokman and A. Quas, A semi-invertible operator Oseledets theorem, Ergodic Theory Dynam. Systems, 34 (2014), 1230-1272.       
5 T. Kato, Perturbation theory for linear operators, Reprint of the 1980 edition, Classics in Mathematics, Springer-Verlag, Berlin, 1995.       
6 Z. Lian and K. Lu, Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space, Mem. Amer. Math. Soc., 206 (2010), vi+106 pp.       
7 R. Mañé, Lyapounov exponents and stable manifolds for compact transformations, in Geometric Dynamics (Rio de Janeiro, 1981), Lecture Notes in Math., 1007, Springer, Berlin, 1983, 522-577.       
8 V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov exponents of dynamical systems, Trudy Moskov. Mat. Obšč., 19 (1968), 179-210.       
9 G. Pisier, The Volume of Convex Bodies and Banach Space Geometry, Cambridge Tracts in Mathematics, No. 94, Cambridge University Press, Cambridge, 1989.
10 M. S. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math., 32 (1979), 356-362.       
11 D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space, Ann. of Math. (2), 115 (1982), 243-290.       
12 P. Thieullen, Fibrés dynamiques asymptotiquement compacts. Exposants de Lyapounov. Entropie. Dimension, Ann. Inst. H. Poincaré Anal. Non Linéaire, 4 (1987), 49-97.       
13 P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Studies in Advanced Mathematics, 25, Cambridge University Press, Cambridge, 1991.       

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