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A note on equivalent definitions of topological transitivity
Admissibility versus nonuniform exponential behavior for noninvertible cocycles
1. | Departamento de Matemática, Instituto Superior Técnico, UTL, 1049-001 Lisboa, Portugal |
2. | Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal |
References:
[1] |
L. Barreira and Ya. Pesin, "Lyapunov Exponents and Smooth Ergodic Theory,", University Lecture Series, 23 (2002).
|
[2] |
L. Barreira and C. Valls, "Stability of Nonautonomous Differential Equations,", Lect. Notes in Math., 1926 (2008).
|
[3] |
C. Chicone and Yu. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations,", Mathematical Surveys and Monographs, 70 (1999).
|
[4] |
Ju. Dalec$'$kiĭ and M. Kreĭn, "Stability of Solutions of Differential Equations in Banach Space,", Translations of Mathematical Monographs, 43 (1974).
|
[5] |
N. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line,, J. Funct. Anal., 235 (2006), 330.
doi: 10.1016/j.jfa.2005.11.002. |
[6] |
B. Levitan and V. Zhikov, "Almost Periodic Functions and Differential Equations,", Cambridge University Press, (1982).
|
[7] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I,, Ann. of Math., 67 (1958), 517.
doi: 10.2307/1969871. |
[8] |
J. Massera and J. Schäffer, "Linear Differential Equations and Function Spaces,", Pure and Applied Mathematics, 21 (1966).
|
[9] |
M. Megan, B. Sasu and A. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces,, Integral Equations Operator Theory, 44 (2002), 71.
doi: 10.1007/BF01197861. |
[10] |
N. Minh and N. Huy, Characterizations of dichotomies of evolution equations on the half-line,, J. Math. Anal. Appl., 261 (2001), 28.
doi: 10.1006/jmaa.2001.7450. |
[11] |
P. Ngoc and T. Naito, New characterizations of exponential dichotomy and exponential stability of linear difference equations,, J. Difference Equ. Appl., 11 (2005), 909.
doi: 10.1080/00423110500211947. |
[12] |
O. Perron, Die Stabilitätsfrage bei Differentialgleichungen,, Math. Z., 32 (1930), 703.
doi: 10.1007/BF01194662. |
[13] |
P. Preda and M. Megan, Nonuniform dichotomy of evolutionary processes in Banach spaces,, Bull. Austral. Math. Soc., 27 (1983), 31.
doi: 10.1017/S0004972700011473. |
[14] |
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.
doi: 10.1007/s00020-002-1268-7. |
[15] |
P. Preda, A. Pogan and C. Preda, Schäffer spaces and uniform exponential stability of linear skew-product semiflows,, J. Differential Equations, 212 (2005), 191.
doi: 10.1016/j.jde.2004.07.019. |
[16] |
P. Preda, A. Pogan and C. Preda, Schäffer spaces and exponential dichotomy for evolutionary processes,, J. Differential Equations, 230 (2006), 378.
doi: 10.1016/j.jde.2006.02.004. |
[17] |
A. Sasu and B. Sasu, Discrete admissibility, $l^p$-spaces and exponential dichotomy on the real line,, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13 (2006), 551.
|
[18] |
A. Sasu and B. Sasu, Exponential dichotomy and $(l^p,l^q)$-admissibility on the half-line,, J. Math. Anal. Appl., 316 (2006), 397.
doi: 10.1016/j.jmaa.2005.04.047. |
[19] |
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.
doi: 10.1007/BF01203774. |
show all references
References:
[1] |
L. Barreira and Ya. Pesin, "Lyapunov Exponents and Smooth Ergodic Theory,", University Lecture Series, 23 (2002).
|
[2] |
L. Barreira and C. Valls, "Stability of Nonautonomous Differential Equations,", Lect. Notes in Math., 1926 (2008).
|
[3] |
C. Chicone and Yu. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations,", Mathematical Surveys and Monographs, 70 (1999).
|
[4] |
Ju. Dalec$'$kiĭ and M. Kreĭn, "Stability of Solutions of Differential Equations in Banach Space,", Translations of Mathematical Monographs, 43 (1974).
|
[5] |
N. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line,, J. Funct. Anal., 235 (2006), 330.
doi: 10.1016/j.jfa.2005.11.002. |
[6] |
B. Levitan and V. Zhikov, "Almost Periodic Functions and Differential Equations,", Cambridge University Press, (1982).
|
[7] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I,, Ann. of Math., 67 (1958), 517.
doi: 10.2307/1969871. |
[8] |
J. Massera and J. Schäffer, "Linear Differential Equations and Function Spaces,", Pure and Applied Mathematics, 21 (1966).
|
[9] |
M. Megan, B. Sasu and A. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces,, Integral Equations Operator Theory, 44 (2002), 71.
doi: 10.1007/BF01197861. |
[10] |
N. Minh and N. Huy, Characterizations of dichotomies of evolution equations on the half-line,, J. Math. Anal. Appl., 261 (2001), 28.
doi: 10.1006/jmaa.2001.7450. |
[11] |
P. Ngoc and T. Naito, New characterizations of exponential dichotomy and exponential stability of linear difference equations,, J. Difference Equ. Appl., 11 (2005), 909.
doi: 10.1080/00423110500211947. |
[12] |
O. Perron, Die Stabilitätsfrage bei Differentialgleichungen,, Math. Z., 32 (1930), 703.
doi: 10.1007/BF01194662. |
[13] |
P. Preda and M. Megan, Nonuniform dichotomy of evolutionary processes in Banach spaces,, Bull. Austral. Math. Soc., 27 (1983), 31.
doi: 10.1017/S0004972700011473. |
[14] |
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.
doi: 10.1007/s00020-002-1268-7. |
[15] |
P. Preda, A. Pogan and C. Preda, Schäffer spaces and uniform exponential stability of linear skew-product semiflows,, J. Differential Equations, 212 (2005), 191.
doi: 10.1016/j.jde.2004.07.019. |
[16] |
P. Preda, A. Pogan and C. Preda, Schäffer spaces and exponential dichotomy for evolutionary processes,, J. Differential Equations, 230 (2006), 378.
doi: 10.1016/j.jde.2006.02.004. |
[17] |
A. Sasu and B. Sasu, Discrete admissibility, $l^p$-spaces and exponential dichotomy on the real line,, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13 (2006), 551.
|
[18] |
A. Sasu and B. Sasu, Exponential dichotomy and $(l^p,l^q)$-admissibility on the half-line,, J. Math. Anal. Appl., 316 (2006), 397.
doi: 10.1016/j.jmaa.2005.04.047. |
[19] |
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.
doi: 10.1007/BF01203774. |
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Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206 |
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