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A concise proof of the multiplicative ergodic theorem on Banach spaces
1. | School of Mathematics and Physics, The University of Queensland, St Lucia QLD 4072, Australia |
2. | Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, B.C., V8W 3R4 |
References:
[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.
doi: 10.1017/S0143385709000339. |
[4] |
C. González-Tokman and A. Quas, A semi-invertible operator Oseledets theorem, Ergodic Theory Dynam. Systems, 34 (2014), 1230-1272.
doi: 10.1017/etds.2012.189. |
[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.
doi: 10.1090/S0065-9266-10-00574-0. |
[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.
doi: 10.1007/BFb0061433. |
[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.
doi: 10.1017/CBO9780511662454. |
[10] |
M. S. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math., 32 (1979), 356-362.
doi: 10.1007/BF02760464. |
[11] |
D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space, Ann. of Math. (2), 115 (1982), 243-290.
doi: 10.2307/1971392. |
[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.
doi: 10.1017/CBO9780511608735. |
show all references
References:
[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.
doi: 10.1017/S0143385709000339. |
[4] |
C. González-Tokman and A. Quas, A semi-invertible operator Oseledets theorem, Ergodic Theory Dynam. Systems, 34 (2014), 1230-1272.
doi: 10.1017/etds.2012.189. |
[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.
doi: 10.1090/S0065-9266-10-00574-0. |
[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.
doi: 10.1007/BFb0061433. |
[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.
doi: 10.1017/CBO9780511662454. |
[10] |
M. S. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math., 32 (1979), 356-362.
doi: 10.1007/BF02760464. |
[11] |
D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space, Ann. of Math. (2), 115 (1982), 243-290.
doi: 10.2307/1971392. |
[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.
doi: 10.1017/CBO9780511608735. |
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