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Critical points of functionalized Lagrangians
Multiplicative ergodic theorem on flag bundles of semi-simple Lie groups
1. | Faculdade de Matemática - Universidade Federal de Uberlândia, Campus Santa Mônica, Av. João Naves de Ávila - 2121 38.408-100, Uberlândia - MG, Brazil |
2. | Imecc - Unicamp, Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz 13083-859, Campinas - SP, Brazil |
References:
[1] |
L. Arnold, "Random Dynamical Systems,", Springer Monographs in Mathematics, (1998).
|
[2] |
L. Arnold, N. D. Cong and V. I. Oseledets, Jordan normal form for linear cocycles,, Random Oper. Stochastic Equations, 7 (1999), 303.
|
[3] |
F. Colonius and W. Kliemann, "The Dynamics of Control,", Birkhäuser, (2000).
doi: 10.1007/978-1-4612-1350-5_3. |
[4] |
J. J. Duistermat, J. A. C. Kolk and V. S. Varadarajan, Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups,, Compositio Math., 49 (1983), 309.
|
[5] |
R. Feres, "Dynamical Systems and Semisimple Groups: An Introduction,", Cambridge University Press, (1998).
doi: 10.5840/ancientphil199818243. |
[6] |
Y. Guivarch, L. Ji and J. C. Taylor, "Compactifications of Symmetric Spaces,", Progress in Mathematics, (1998).
|
[7] |
S. Helgason, "Groups and Geometric Analysis,", Academic Press, (1984).
|
[8] |
J. Hilgert and G. Ólafsson, "Causal Symmetric Spaces,", Geometry and Harmonic Analysis, 18 (1997).
|
[9] |
V. A. Kaimanovich, Lyapunov exponents, symmetric spaces and multiplicative ergodic theorem for semisimple lie groups,, J. Soviet Math., 47 (1989), 2387.
doi: 10.1007/BF01840421. |
[10] |
A. Karlsson and G. A. Margulis, A multiplicative ergodic theorem and nonpositively curved spaces,, Communications in Mathematical Physics, 208 (1999), 107.
doi: 10.1007/s002200050750. |
[11] |
A. W. Knapp, "Lie Groups: Beyond an Introduction,", Second Edition, 140 (2004).
|
[12] |
G. Link, "Limit Sets of Discrete Groups Acting on Symmetric Spaces,", Ph.D thesis, (2002). Google Scholar |
[13] |
S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry,", vol. I, (1963).
|
[14] |
M. S. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem,, Israel J. Math., 32 (1979), 356.
|
[15] |
D. Ruelle, Ergodic theory of differentiable dynamical systems,, Publ. Math. IHES, 50 (1979), 27.
doi: 10.1007/BF00587200. |
[16] |
L. A. B. San Martin, Maximal semigroups in semi-simple lie groups,, Trans. Amer. Math. Soc., 353 (2001), 5165.
|
[17] |
L. A. B. San Martin, Nonexistence of invariant semigroups in affine symmetric spaces,, Math. Ann., 321 (2001), 587.
doi: 10.1016/S0039-6028(01)00812-3. |
[18] |
L. A. B. San Martin and L. Seco, Morse and Lyapunov spectra and dynamics on flag bundles,, Ergodic Theory & Dynamical Systems, 30 (2010), 893.
doi: 10.1017/S0143385709000285. |
[19] |
G. Warner, "Harmonic Analysis on Semi-simple Lie Groups I,", Springer-Verlag, (1972).
doi: 10.1007/978-3-642-50275-0. |
[20] |
R.Zimmer, Ergodic theory and semisimple groups,, Monographs in Mathematics, 81 (1984).
|
show all references
References:
[1] |
L. Arnold, "Random Dynamical Systems,", Springer Monographs in Mathematics, (1998).
|
[2] |
L. Arnold, N. D. Cong and V. I. Oseledets, Jordan normal form for linear cocycles,, Random Oper. Stochastic Equations, 7 (1999), 303.
|
[3] |
F. Colonius and W. Kliemann, "The Dynamics of Control,", Birkhäuser, (2000).
doi: 10.1007/978-1-4612-1350-5_3. |
[4] |
J. J. Duistermat, J. A. C. Kolk and V. S. Varadarajan, Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups,, Compositio Math., 49 (1983), 309.
|
[5] |
R. Feres, "Dynamical Systems and Semisimple Groups: An Introduction,", Cambridge University Press, (1998).
doi: 10.5840/ancientphil199818243. |
[6] |
Y. Guivarch, L. Ji and J. C. Taylor, "Compactifications of Symmetric Spaces,", Progress in Mathematics, (1998).
|
[7] |
S. Helgason, "Groups and Geometric Analysis,", Academic Press, (1984).
|
[8] |
J. Hilgert and G. Ólafsson, "Causal Symmetric Spaces,", Geometry and Harmonic Analysis, 18 (1997).
|
[9] |
V. A. Kaimanovich, Lyapunov exponents, symmetric spaces and multiplicative ergodic theorem for semisimple lie groups,, J. Soviet Math., 47 (1989), 2387.
doi: 10.1007/BF01840421. |
[10] |
A. Karlsson and G. A. Margulis, A multiplicative ergodic theorem and nonpositively curved spaces,, Communications in Mathematical Physics, 208 (1999), 107.
doi: 10.1007/s002200050750. |
[11] |
A. W. Knapp, "Lie Groups: Beyond an Introduction,", Second Edition, 140 (2004).
|
[12] |
G. Link, "Limit Sets of Discrete Groups Acting on Symmetric Spaces,", Ph.D thesis, (2002). Google Scholar |
[13] |
S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry,", vol. I, (1963).
|
[14] |
M. S. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem,, Israel J. Math., 32 (1979), 356.
|
[15] |
D. Ruelle, Ergodic theory of differentiable dynamical systems,, Publ. Math. IHES, 50 (1979), 27.
doi: 10.1007/BF00587200. |
[16] |
L. A. B. San Martin, Maximal semigroups in semi-simple lie groups,, Trans. Amer. Math. Soc., 353 (2001), 5165.
|
[17] |
L. A. B. San Martin, Nonexistence of invariant semigroups in affine symmetric spaces,, Math. Ann., 321 (2001), 587.
doi: 10.1016/S0039-6028(01)00812-3. |
[18] |
L. A. B. San Martin and L. Seco, Morse and Lyapunov spectra and dynamics on flag bundles,, Ergodic Theory & Dynamical Systems, 30 (2010), 893.
doi: 10.1017/S0143385709000285. |
[19] |
G. Warner, "Harmonic Analysis on Semi-simple Lie Groups I,", Springer-Verlag, (1972).
doi: 10.1007/978-3-642-50275-0. |
[20] |
R.Zimmer, Ergodic theory and semisimple groups,, Monographs in Mathematics, 81 (1984).
|
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