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Noninvertible cocycles: Robustness of exponential dichotomies
1. | Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa |
2. | Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa |
References:
[1] |
L. Barreira and Ya. Pesin, "Nonuniform Hyperbolicity," Encyclopedia of Math. and Its Appl. 115, Cambridge Univ. Press, 2007. |
[2] |
L. Barreira and C. Valls, Stability theory and Lyapunov regularity, J. Differential Equations, 232 (2007), 675-701.
doi: 10.1016/j.jde.2006.09.021. |
[3] |
L. Barreira and C. Valls, Robustness of nonuniform exponential dichotomies in Banach spaces, J. Differential Equations, 244 (2008), 2407-2447.
doi: 10.1016/j.jde.2008.02.028. |
[4] |
L. Barreira and C. Valls, "Stability of Nonautonomous Differential Equations," Lect. Notes in Math. 1926, Springer, 2008. |
[5] |
L. Barreira and C. Valls, Robustness of discrete dynamics via Lyapunov sequences, Comm. Math. Phys., 290 (2009), 219-238.
doi: 10.1007/s00220-009-0762-z. |
[6] |
L. Barreira and C. Valls, Robust nonuniform dichotomies and parameter dependence, J. Math. Anal. Appl., 373 (2011), 690-708.
doi: 10.1016/j.jmaa.2010.08.026. |
[7] |
C. Chicone and Yu. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Mathematical Surveys and Monographs 70, Amer. Math. Soc., 1999. |
[8] |
S.-N. Chow and H. Leiva, Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces, J. Differential Equations, 120 (1995), 429-477.
doi: 10.1006/jdeq.1995.1117. |
[9] |
W. Coppel, Dichotomies and reducibility, J. Differential Equations, 3 (1967), 500-521. |
[10] |
W. Coppel, "Dichotomies in Stability Theory," Lect. Notes in Math. 629, Springer, 1978. |
[11] |
Ju. Dalec$'$kiĭ and M. Kreĭn, "Stability of Solutions of Differential Equations in Banach Space," Translations of Mathematical Monographs 43, Amer. Math. Soc., 1974. |
[12] |
J. Hale, "Asymptotic Behavior of Dissipative Systems," Mathematical Surveys and Monographs 25, Amer. Math. Soc., 1988. |
[13] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lect. Notes in Math. 840, Springer, 1981. |
[14] |
N. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line, J. Funct. Anal., 235 (2006), 330-354.
doi: 10.1016/j.jfa.2005.11.002. |
[15] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I, Ann. of Math., 67 (1958), 517-573.
doi: 10.2307/1969871. |
[16] |
J. Massera and J. Schäffer, "Linear Differential Equations and Function Spaces," Pure and Applied Mathematics, 21, Academic Press, 1966. |
[17] |
R. Naulin and M. Pinto, Stability of discrete dichotomies for linear difference systems, J. Differ. Equations Appl., 3 (1997), 101-123. |
[18] |
R. Naulin and M. Pinto, Admissible perturbations of exponential dichotomy roughness, Nonlinear Anal., 31 (1998), 559-571.
doi: 10.1016/S0362-546X(97)00423-9. |
[19] |
O. Perron, Die Stabilit\"atsfrage bei Differentialgleichungen, Math. Z., 32 (1930), 703-728.
doi: 10.1007/BF01194662. |
[20] |
V. Pliss and G. Sell, Robustness of exponential dichotomies ininfinite-dimensional dynamical systems, J. Dynam. Differential Equations, 11 (1999), 471-513.
doi: 10.1023/A:1021913903923. |
[21] |
L. Popescu, Exponential dichotomy roughness on Banach spaces, J. Math. Anal. Appl., 314 (2006), 436-454.
doi: 10.1016/j.jmaa.2005.04.011. |
[22] |
A. Sasu, Exponential dichotomy and dichotomy radius for difference equations, J. Math. Anal. Appl., 344 (2008), 906-920.
doi: 10.1016/j.jmaa.2008.03.019. |
[23] |
B. Sasu and A. Sasu, Input-output conditions for the asymptotic behavior of linear skew-product flows and applications, Commun. Pure Appl. Anal., 5 (2006), 551-569. |
[24] |
G. Sell and Y. You, "Dynamics of Evolutionary Equations," Applied Mathematical Sciences 143, Springer, 2002. |
show all references
References:
[1] |
L. Barreira and Ya. Pesin, "Nonuniform Hyperbolicity," Encyclopedia of Math. and Its Appl. 115, Cambridge Univ. Press, 2007. |
[2] |
L. Barreira and C. Valls, Stability theory and Lyapunov regularity, J. Differential Equations, 232 (2007), 675-701.
doi: 10.1016/j.jde.2006.09.021. |
[3] |
L. Barreira and C. Valls, Robustness of nonuniform exponential dichotomies in Banach spaces, J. Differential Equations, 244 (2008), 2407-2447.
doi: 10.1016/j.jde.2008.02.028. |
[4] |
L. Barreira and C. Valls, "Stability of Nonautonomous Differential Equations," Lect. Notes in Math. 1926, Springer, 2008. |
[5] |
L. Barreira and C. Valls, Robustness of discrete dynamics via Lyapunov sequences, Comm. Math. Phys., 290 (2009), 219-238.
doi: 10.1007/s00220-009-0762-z. |
[6] |
L. Barreira and C. Valls, Robust nonuniform dichotomies and parameter dependence, J. Math. Anal. Appl., 373 (2011), 690-708.
doi: 10.1016/j.jmaa.2010.08.026. |
[7] |
C. Chicone and Yu. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Mathematical Surveys and Monographs 70, Amer. Math. Soc., 1999. |
[8] |
S.-N. Chow and H. Leiva, Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces, J. Differential Equations, 120 (1995), 429-477.
doi: 10.1006/jdeq.1995.1117. |
[9] |
W. Coppel, Dichotomies and reducibility, J. Differential Equations, 3 (1967), 500-521. |
[10] |
W. Coppel, "Dichotomies in Stability Theory," Lect. Notes in Math. 629, Springer, 1978. |
[11] |
Ju. Dalec$'$kiĭ and M. Kreĭn, "Stability of Solutions of Differential Equations in Banach Space," Translations of Mathematical Monographs 43, Amer. Math. Soc., 1974. |
[12] |
J. Hale, "Asymptotic Behavior of Dissipative Systems," Mathematical Surveys and Monographs 25, Amer. Math. Soc., 1988. |
[13] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lect. Notes in Math. 840, Springer, 1981. |
[14] |
N. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line, J. Funct. Anal., 235 (2006), 330-354.
doi: 10.1016/j.jfa.2005.11.002. |
[15] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I, Ann. of Math., 67 (1958), 517-573.
doi: 10.2307/1969871. |
[16] |
J. Massera and J. Schäffer, "Linear Differential Equations and Function Spaces," Pure and Applied Mathematics, 21, Academic Press, 1966. |
[17] |
R. Naulin and M. Pinto, Stability of discrete dichotomies for linear difference systems, J. Differ. Equations Appl., 3 (1997), 101-123. |
[18] |
R. Naulin and M. Pinto, Admissible perturbations of exponential dichotomy roughness, Nonlinear Anal., 31 (1998), 559-571.
doi: 10.1016/S0362-546X(97)00423-9. |
[19] |
O. Perron, Die Stabilit\"atsfrage bei Differentialgleichungen, Math. Z., 32 (1930), 703-728.
doi: 10.1007/BF01194662. |
[20] |
V. Pliss and G. Sell, Robustness of exponential dichotomies ininfinite-dimensional dynamical systems, J. Dynam. Differential Equations, 11 (1999), 471-513.
doi: 10.1023/A:1021913903923. |
[21] |
L. Popescu, Exponential dichotomy roughness on Banach spaces, J. Math. Anal. Appl., 314 (2006), 436-454.
doi: 10.1016/j.jmaa.2005.04.011. |
[22] |
A. Sasu, Exponential dichotomy and dichotomy radius for difference equations, J. Math. Anal. Appl., 344 (2008), 906-920.
doi: 10.1016/j.jmaa.2008.03.019. |
[23] |
B. Sasu and A. Sasu, Input-output conditions for the asymptotic behavior of linear skew-product flows and applications, Commun. Pure Appl. Anal., 5 (2006), 551-569. |
[24] |
G. Sell and Y. You, "Dynamics of Evolutionary Equations," Applied Mathematical Sciences 143, Springer, 2002. |
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