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Nonuniform exponential dichotomies and admissibility
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, "Lyapunov Exponents and Smooth Ergodic Theory," University Lecture Series 23, Amer. Math. Soc., 2002. |
[2] |
L. Barreira and Ya. Pesin, "Nonuniform Hyperbolicity," Encyclopedia of Math. and Its Appl. 115, Cambridge Univ. Press, 2007. |
[3] |
L. Barreira and J. Schmeling, Sets of "non-typical" points have full topological entropy and full Hausdorff dimension, Israel J. Math., 116 (2000), 29-70.
doi: 10.1007/BF02773211. |
[4] |
L. Barreira and C. Valls, "Stability of Nonautonomous Differential Equations," Lect. Notes in Math. 1926, Springer, 2008. |
[5] |
L. Barreira and C. Valls, Admissibility for nonuniform exponential contractions, J. Differential Equations, 249 (2010), 2889-2904.
doi: 10.1016/j.jde.2010.06.010. |
[6] |
C. Chicone and Yu. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Mathematical Surveys and Monographs 70, Amer. Math. Soc., 1999. |
[7] |
Ju. Dalec'kiĭ and M. Kreĭn, "Stability of Solutions of Differential Equations in Banach Space," Translations of Mathematical Monographs 43, Amer. Math. Soc., 1974. |
[8] |
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. |
[9] |
B. Levitan and V. Zhikov, "Almost Periodic Functions and Differential Equations," Cambridge University Press, 1982. |
[10] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I, Ann. of Math. (2), 67 (1958), 517-573.
doi: 10.2307/1969871. |
[11] |
J. Massera and J. Schäffer, "Linear Differential Equations and Function Spaces," Pure and Applied Mathematics 21, Academic Press, 1966. |
[12] |
M. Megan, B. Sasu and A. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces, Integral Equations Operator Theory, 44 (2002), 71-78.
doi: 10.1007/BF01197861. |
[13] |
N. Minh and N. Huy, Characterizations of dichotomies of evolution equations on the half-line, J. Math. Anal. Appl., 261 (2001), 28-44.
doi: 10.1006/jmaa.2001.7450. |
[14] |
V. Oseledets, A multiplicative ergodic theorem. Liapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc., 19 (1968), 197-221. |
[15] |
O. Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z., 32 (1930), 703-728.
doi: 10.1007/BF01194662. |
[16] |
Ya. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents, Math. USSR-Izv., 10 (1976), 1261-1305.
doi: 10.1070/IM1976v010n06ABEH001835. |
[17] |
P. Preda and M. Megan, Nonuniform dichotomy of evolutionary processes in Banach spaces, Bull. Austral. Math. Soc., 27 (1983), 31-52.
doi: 10.1017/S0004972700011473. |
[18] |
P. Preda, A. Pogan and C. Preda, $(L^p,L^q)$-admissibility and exponential dichotomy of evolutionary processes on the half-line, Integral Equations Operator Theory, 49 (2004), 405-418.
doi: 10.1007/s00020-002-1268-7. |
[19] |
P. Preda, A. Pogan and C. Preda, Schäffer spaces and exponential dichotomy for evolutionary processes, J. Differential Equations, 230 (2006), 378-391.
doi: 10.1016/j.jde.2006.02.004. |
[20] |
J. Schäffer, Function spaces with translations, Math. Ann., 137 (1959), 209-262.
doi: 10.1007/BF01343353. |
[21] |
N. Van Minh, F. Räbiger and R. Schnaubelt, Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line, Integral Equations Operator Theory, 32 (1998), 332-353.
doi: 10.1007/BF01203774. |
show all references
References:
[1] |
L. Barreira and Ya. Pesin, "Lyapunov Exponents and Smooth Ergodic Theory," University Lecture Series 23, Amer. Math. Soc., 2002. |
[2] |
L. Barreira and Ya. Pesin, "Nonuniform Hyperbolicity," Encyclopedia of Math. and Its Appl. 115, Cambridge Univ. Press, 2007. |
[3] |
L. Barreira and J. Schmeling, Sets of "non-typical" points have full topological entropy and full Hausdorff dimension, Israel J. Math., 116 (2000), 29-70.
doi: 10.1007/BF02773211. |
[4] |
L. Barreira and C. Valls, "Stability of Nonautonomous Differential Equations," Lect. Notes in Math. 1926, Springer, 2008. |
[5] |
L. Barreira and C. Valls, Admissibility for nonuniform exponential contractions, J. Differential Equations, 249 (2010), 2889-2904.
doi: 10.1016/j.jde.2010.06.010. |
[6] |
C. Chicone and Yu. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Mathematical Surveys and Monographs 70, Amer. Math. Soc., 1999. |
[7] |
Ju. Dalec'kiĭ and M. Kreĭn, "Stability of Solutions of Differential Equations in Banach Space," Translations of Mathematical Monographs 43, Amer. Math. Soc., 1974. |
[8] |
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. |
[9] |
B. Levitan and V. Zhikov, "Almost Periodic Functions and Differential Equations," Cambridge University Press, 1982. |
[10] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I, Ann. of Math. (2), 67 (1958), 517-573.
doi: 10.2307/1969871. |
[11] |
J. Massera and J. Schäffer, "Linear Differential Equations and Function Spaces," Pure and Applied Mathematics 21, Academic Press, 1966. |
[12] |
M. Megan, B. Sasu and A. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces, Integral Equations Operator Theory, 44 (2002), 71-78.
doi: 10.1007/BF01197861. |
[13] |
N. Minh and N. Huy, Characterizations of dichotomies of evolution equations on the half-line, J. Math. Anal. Appl., 261 (2001), 28-44.
doi: 10.1006/jmaa.2001.7450. |
[14] |
V. Oseledets, A multiplicative ergodic theorem. Liapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc., 19 (1968), 197-221. |
[15] |
O. Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z., 32 (1930), 703-728.
doi: 10.1007/BF01194662. |
[16] |
Ya. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents, Math. USSR-Izv., 10 (1976), 1261-1305.
doi: 10.1070/IM1976v010n06ABEH001835. |
[17] |
P. Preda and M. Megan, Nonuniform dichotomy of evolutionary processes in Banach spaces, Bull. Austral. Math. Soc., 27 (1983), 31-52.
doi: 10.1017/S0004972700011473. |
[18] |
P. Preda, A. Pogan and C. Preda, $(L^p,L^q)$-admissibility and exponential dichotomy of evolutionary processes on the half-line, Integral Equations Operator Theory, 49 (2004), 405-418.
doi: 10.1007/s00020-002-1268-7. |
[19] |
P. Preda, A. Pogan and C. Preda, Schäffer spaces and exponential dichotomy for evolutionary processes, J. Differential Equations, 230 (2006), 378-391.
doi: 10.1016/j.jde.2006.02.004. |
[20] |
J. Schäffer, Function spaces with translations, Math. Ann., 137 (1959), 209-262.
doi: 10.1007/BF01343353. |
[21] |
N. Van Minh, F. Räbiger and R. Schnaubelt, Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line, Integral Equations Operator Theory, 32 (1998), 332-353.
doi: 10.1007/BF01203774. |
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