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Invariant foliations for random dynamical systems
1. | Institute for Mathematics and its Application, University of Minnesota, Minneapolis, MN, 55455, United States |
2. | Department of Mathematics, Brigham Young University, Provo, Utah 84602 |
3. | Department of Mathematics, Michigan State University, East Lansing, MI 48824 |
References:
[1] |
L. M. Arnold, Random Dynamical Systems, Springer, New York, 1998. |
[2] |
P. Bates, K. Lu and C. Zeng, Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space, Memoirs of the AMS, 135 1998, viii+129 pp.
doi: 10.1090/memo/0645. |
[3] |
P. Bates, K. Lu and C. Zeng, Persistence of overflowing manifold for semiflow, Comm. Pure Appl. Math., 52 (1999), 983-1046.
doi: 10.1002/(SICI)1097-0312(199908)52:8<983::AID-CPA4>3.0.CO;2-O. |
[4] |
P. Bates, K. Lu and C. Zeng, Invariant foliations near normally hyperbolic invariant manifolds for semiflows, Trans. Amer. Math. Soc., 352 (2000), 4641-4676.
doi: 10.1090/S0002-9947-00-02503-4. |
[5] |
T. Caraballo, J. Duan, K. Lu and B. Schmalfuss, Invariant manifolds for random and stochastic partial differential equations, Adv. Nonlinear Stud., 10 (2010), 23-52. |
[6] |
C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, LNM 580. Springer-Verlag, Berlin-Heidelberg-New York, 1977. |
[7] |
S-N. Chow, K. Lu and X-B. Lin, Smooth foliations for flows in banach space, Journal of Differential Equations, 94 (1991), 266-291.
doi: 10.1016/0022-0396(91)90093-O. |
[8] |
P. Drabek and J. Milota, Methods of Nonlinear Analysis Applications to Differential Equations, Birkhäuser Verlag, Basel, 2007. |
[9] |
N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. Journal, 21 (1971), 193-226.
doi: 10.1512/iumj.1972.21.21017. |
[10] |
N. Fenichel, Asymptotic stability with rate conditions, Indiana Univ. Math. Journal, 23 (1974), 1109-1137. |
[11] |
N. Fenichel, Asymptotic stability with rate conditions II, Indiana Univ. Math. Journal, 26 (1977), 81-93.
doi: 10.1512/iumj.1977.26.26006. |
[12] |
J. Hadamard, Sur l'iteration et les solutions asymptotiques des equations defferentielles, Bull. Soc. Math. France, 29 (1901), 224-228. |
[13] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, 583, Springer-Verlag, New York, 1977. |
[14] |
C. K. R. T. Jones and N. Kopell, Tracking invariant manifolds with differential forms in singularly perturbed systems, J. Differential Equations, 108 (1994), 64-88.
doi: 10.1006/jdeq.1994.1025. |
[15] |
J. Li, K. Lu and P. Bates, Normally hyperbolic invariant manifolds for random dynamical systems, Trans. Amer. Math. Soc., 365 (2013), 5933-5966.
doi: 10.1090/S0002-9947-2013-05825-4. |
[16] |
P-D. Liu and M. Qian, Smooth Ergodic Theory of Random Dynamical Systems, Lecture Notes in Mathematics, 1606. Springer-Verlag, Berlin, 1995. |
[17] |
R. Mañé, Liapunov exponents and stable manifolds for compact transformations, Geometrical dynamics, Lecture Notes in Math., Springer Verlag, New York, 1007 (1983), 522-577.
doi: 10.1007/BFb0061433. |
[18] |
W. Li and K. Lu, Sternberg theorems for random dynamical systems, Comm. Pure Appl. Math., 58 (2005), 941-988.
doi: 10.1002/cpa.20083. |
[19] |
Z. Lian and K. Lu, Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space, Memoirs of the AMS., 206 (2010), vi+106 pp.
doi: 10.1090/S0065-9266-10-00574-0. |
[20] |
K. Lu and B. Schmalfuss, Invariant foliations for stochastic partial differential equations, Stoch. Dyn., 8 (2008), 505-518.
doi: 10.1142/S0219493708002421. |
[21] |
Y. Pesin, Characteristic Lyapunov exponents, and smooth ergodic theory, Russian Math. Surveys, 32 (1977), 55-112. |
[22] |
D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert spaces, Ann. of Math., 115 (1982), 243-290.
doi: 10.2307/1971392. |
[23] |
T. Wanner, Linearization of random dynamical systems, Dynamics Reported,, Springer-Verlag, New York, 4 (1995), 203-269. |
[24] |
H. Whitney, Differential manifolds, Ann. of Math., 37 (1936), 645-680.
doi: 10.2307/1968482. |
show all references
References:
[1] |
L. M. Arnold, Random Dynamical Systems, Springer, New York, 1998. |
[2] |
P. Bates, K. Lu and C. Zeng, Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space, Memoirs of the AMS, 135 1998, viii+129 pp.
doi: 10.1090/memo/0645. |
[3] |
P. Bates, K. Lu and C. Zeng, Persistence of overflowing manifold for semiflow, Comm. Pure Appl. Math., 52 (1999), 983-1046.
doi: 10.1002/(SICI)1097-0312(199908)52:8<983::AID-CPA4>3.0.CO;2-O. |
[4] |
P. Bates, K. Lu and C. Zeng, Invariant foliations near normally hyperbolic invariant manifolds for semiflows, Trans. Amer. Math. Soc., 352 (2000), 4641-4676.
doi: 10.1090/S0002-9947-00-02503-4. |
[5] |
T. Caraballo, J. Duan, K. Lu and B. Schmalfuss, Invariant manifolds for random and stochastic partial differential equations, Adv. Nonlinear Stud., 10 (2010), 23-52. |
[6] |
C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, LNM 580. Springer-Verlag, Berlin-Heidelberg-New York, 1977. |
[7] |
S-N. Chow, K. Lu and X-B. Lin, Smooth foliations for flows in banach space, Journal of Differential Equations, 94 (1991), 266-291.
doi: 10.1016/0022-0396(91)90093-O. |
[8] |
P. Drabek and J. Milota, Methods of Nonlinear Analysis Applications to Differential Equations, Birkhäuser Verlag, Basel, 2007. |
[9] |
N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. Journal, 21 (1971), 193-226.
doi: 10.1512/iumj.1972.21.21017. |
[10] |
N. Fenichel, Asymptotic stability with rate conditions, Indiana Univ. Math. Journal, 23 (1974), 1109-1137. |
[11] |
N. Fenichel, Asymptotic stability with rate conditions II, Indiana Univ. Math. Journal, 26 (1977), 81-93.
doi: 10.1512/iumj.1977.26.26006. |
[12] |
J. Hadamard, Sur l'iteration et les solutions asymptotiques des equations defferentielles, Bull. Soc. Math. France, 29 (1901), 224-228. |
[13] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, 583, Springer-Verlag, New York, 1977. |
[14] |
C. K. R. T. Jones and N. Kopell, Tracking invariant manifolds with differential forms in singularly perturbed systems, J. Differential Equations, 108 (1994), 64-88.
doi: 10.1006/jdeq.1994.1025. |
[15] |
J. Li, K. Lu and P. Bates, Normally hyperbolic invariant manifolds for random dynamical systems, Trans. Amer. Math. Soc., 365 (2013), 5933-5966.
doi: 10.1090/S0002-9947-2013-05825-4. |
[16] |
P-D. Liu and M. Qian, Smooth Ergodic Theory of Random Dynamical Systems, Lecture Notes in Mathematics, 1606. Springer-Verlag, Berlin, 1995. |
[17] |
R. Mañé, Liapunov exponents and stable manifolds for compact transformations, Geometrical dynamics, Lecture Notes in Math., Springer Verlag, New York, 1007 (1983), 522-577.
doi: 10.1007/BFb0061433. |
[18] |
W. Li and K. Lu, Sternberg theorems for random dynamical systems, Comm. Pure Appl. Math., 58 (2005), 941-988.
doi: 10.1002/cpa.20083. |
[19] |
Z. Lian and K. Lu, Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space, Memoirs of the AMS., 206 (2010), vi+106 pp.
doi: 10.1090/S0065-9266-10-00574-0. |
[20] |
K. Lu and B. Schmalfuss, Invariant foliations for stochastic partial differential equations, Stoch. Dyn., 8 (2008), 505-518.
doi: 10.1142/S0219493708002421. |
[21] |
Y. Pesin, Characteristic Lyapunov exponents, and smooth ergodic theory, Russian Math. Surveys, 32 (1977), 55-112. |
[22] |
D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert spaces, Ann. of Math., 115 (1982), 243-290.
doi: 10.2307/1971392. |
[23] |
T. Wanner, Linearization of random dynamical systems, Dynamics Reported,, Springer-Verlag, New York, 4 (1995), 203-269. |
[24] |
H. Whitney, Differential manifolds, Ann. of Math., 37 (1936), 645-680.
doi: 10.2307/1968482. |
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