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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, Springer-Verlag, 1998. |
[2] |
L. Arnold, N. D. Cong and V. I. Oseledets, Jordan normal form for linear cocycles, Random Oper. Stochastic Equations, 7 (1999), 303-358. |
[3] |
F. Colonius and W. Kliemann, "The Dynamics of Control," Birkhäuser, Boston, 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), 309-398. |
[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, 156. Birkhser Boston, 1998. |
[7] |
S. Helgason, "Groups and Geometric Analysis," Academic Press, 1984. |
[8] |
J. Hilgert and G. Ólafsson, "Causal Symmetric Spaces," Geometry and Harmonic Analysis, Perspectives in Mathematics, 18, Academic Press, 1997. |
[9] |
V. A. Kaimanovich, Lyapunov exponents, symmetric spaces and multiplicative ergodic theorem for semisimple lie groups, J. Soviet Math., 47 (1989), 2387-2398.
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), 107-123.
doi: 10.1007/s002200050750. |
[11] |
A. W. Knapp, "Lie Groups: Beyond an Introduction," Second Edition, Progress in Mathematics, 140, Birkhäuser, 2004. |
[12] |
G. Link, "Limit Sets of Discrete Groups Acting on Symmetric Spaces," Ph.D thesis, Fakultät für Mathematik der Universität Karlsruhe, 2002. |
[13] |
S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry," vol. I, Interscience Publishe, 1963. |
[14] |
M. S. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math., 32 (1979), 356-362. |
[15] |
D. Ruelle, Ergodic theory of differentiable dynamical systems, Publ. Math. IHES, 50 (1979), 27-58.
doi: 10.1007/BF00587200. |
[16] |
L. A. B. San Martin, Maximal semigroups in semi-simple lie groups, Trans. Amer. Math. Soc., 353 (2001), 5165-5184. |
[17] |
L. A. B. San Martin, Nonexistence of invariant semigroups in affine symmetric spaces, Math. Ann., 321 (2001), 587-600.
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), 893-922.
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, Birkäuser, 1984. |
show all references
References:
[1] |
L. Arnold, "Random Dynamical Systems," Springer Monographs in Mathematics, Springer-Verlag, 1998. |
[2] |
L. Arnold, N. D. Cong and V. I. Oseledets, Jordan normal form for linear cocycles, Random Oper. Stochastic Equations, 7 (1999), 303-358. |
[3] |
F. Colonius and W. Kliemann, "The Dynamics of Control," Birkhäuser, Boston, 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), 309-398. |
[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, 156. Birkhser Boston, 1998. |
[7] |
S. Helgason, "Groups and Geometric Analysis," Academic Press, 1984. |
[8] |
J. Hilgert and G. Ólafsson, "Causal Symmetric Spaces," Geometry and Harmonic Analysis, Perspectives in Mathematics, 18, Academic Press, 1997. |
[9] |
V. A. Kaimanovich, Lyapunov exponents, symmetric spaces and multiplicative ergodic theorem for semisimple lie groups, J. Soviet Math., 47 (1989), 2387-2398.
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), 107-123.
doi: 10.1007/s002200050750. |
[11] |
A. W. Knapp, "Lie Groups: Beyond an Introduction," Second Edition, Progress in Mathematics, 140, Birkhäuser, 2004. |
[12] |
G. Link, "Limit Sets of Discrete Groups Acting on Symmetric Spaces," Ph.D thesis, Fakultät für Mathematik der Universität Karlsruhe, 2002. |
[13] |
S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry," vol. I, Interscience Publishe, 1963. |
[14] |
M. S. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math., 32 (1979), 356-362. |
[15] |
D. Ruelle, Ergodic theory of differentiable dynamical systems, Publ. Math. IHES, 50 (1979), 27-58.
doi: 10.1007/BF00587200. |
[16] |
L. A. B. San Martin, Maximal semigroups in semi-simple lie groups, Trans. Amer. Math. Soc., 353 (2001), 5165-5184. |
[17] |
L. A. B. San Martin, Nonexistence of invariant semigroups in affine symmetric spaces, Math. Ann., 321 (2001), 587-600.
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), 893-922.
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, Birkäuser, 1984. |
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