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Discrete admissibility and exponential trichotomy of dynamical systems
1. | Faculty of Mathematics and Computer Science, West University of Timişoara, V. Pârvan Blvd. No. 4, 300223 Timişoara, Romania |
References:
[1] |
A. I. Alonso, J. Hong and R. Obaya, Exponential dichotomy and trichotomy for difference equations, Comput. Math. Appl., 38 (1999), 41-49.
doi: 10.1016/S0898-1221(99)00167-4. |
[2] |
L. Barreira and C. Valls, Center manifolds for nonuniformly partially hyperbolic diffeomorphisms, J. Math. Pures Appl. (9), 84 (2005), 1693-1715.
doi: 10.1016/j.matpur.2005.07.005. |
[3] |
L. Barreira and C. Valls, Center manifolds for infinite delay, J. Differential Equations, 247 (2009), 1297-1310.
doi: 10.1016/j.jde.2009.04.006. |
[4] |
L. Barreira and C. Valls, Robustness of nonuniform exponential trichotomies in Banach spaces, J. Math. Anal. Appl., 351 (2009), 373-381.
doi: 10.1016/j.jmaa.2008.10.030. |
[5] |
L. Barreira and C. Valls, Lyapunov functions for trichotomies with growth rates, J. Differential Equations, 248 (2010), 151-183.
doi: 10.1016/j.jde.2009.07.001. |
[6] |
L. Barreira and C. Valls, Nonuniform exponential dichotomies and admissibility, Discrete Contin. Dyn. Syst., 30 (2011), 39-53.
doi: 10.3934/dcds.2011.30.39. |
[7] |
L. Barreira and C. Valls, Admissibility versus nonuniform exponential behavior for noninver-tible cocycles, Discrete Contin. Dyn. Syst., 33 (2013), 1297-1311. |
[8] |
C. V. Coffman and J. J. Schäffer, Dichotomies for linear difference equations, Math. Ann., 172 (1967), 139-166.
doi: 10.1007/BF01350095. |
[9] |
S.-N. Chow and H. Leiva, Existence and roughness of the exponential dichotomy for linear skew-product semiflows in Banach spaces, J. Differential Equations, 120 (1995), 429-477.
doi: 10.1006/jdeq.1995.1117. |
[10] |
Ju. L. Dalec'kiĭ and M. G. Kreĭn, Stability of Solutions of Differential Equations in Banach Spaces, Trans. Math. Monographs, Vol. 43, Amer. Math. Soc., Providence R.I., 1974. |
[11] |
S. Elaydi and O. Hájek, Some remarks on nonlinear dichotomy and trichotomy, in Non-linear Analysis and Applications (Arlington, Tex., 1986), Lect. Notes Pure Appl. Math., 109, Dekker, New York, (1987), 175-178. |
[12] |
S. Elaydi and O. Hájek, Exponential trichotomy of differential systems, J. Math. Anal. Appl., 129 (1988), 362-374.
doi: 10.1016/0022-247X(88)90255-7. |
[13] |
S. Elaydi and O. Hájek, Exponential dichotomy and trichotomy of nonlinear differential equations, Differ. Integral Equ., 3 (1990), 1201-1224. |
[14] |
S. Elaydi and K. Janglajew, Dichotomy and trichotomy of difference equations, J. Differ. Equations Appl., 3 (1998), 417-448.
doi: 10.1080/10236199708808113. |
[15] |
N. T. Huy and N. Van Minh, Exponential dichotomy of difference equations and applications to evolution equations on the half-line, Comput. Math. Appl., 42 (2001), 301-311.
doi: 10.1016/S0898-1221(01)00155-9. |
[16] |
J. López-Fenner and M. Pinto, $(h,k)$-trichotomies and asymptotics of nonautonomous difference equations, Comp. Math. Appl., 33 (1997), 105-124.
doi: 10.1016/S0898-1221(97)00080-1. |
[17] |
J. L. Massera and J. J. Schäffer, Linear Differential Equations and Function Spaces, Pure and Applied Mathematics, Vol. 21, Academic Press, New York-London, 1966. |
[18] |
M. Megan, A. L. Sasu and B. Sasu, Discrete admissibility and exponential dichotomy for evolution families, Discrete Contin. Dyn. Syst., 9 (2003), 383-397. |
[19] |
N. Van Minh and N. T. 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. |
[20] |
O. Perron, Die Stabilitätsfrage bei Differentialgleischungen, Math. Z., 32 (1930), 703-728.
doi: 10.1007/BF01194662. |
[21] |
K. J. Palmer, Exponential dichotomy and expansivity, Ann. Mat. Pura Appl. (4), 185 (2006), S171-S185.
doi: 10.1007/s10231-004-0141-5. |
[22] |
V. A. Pliss and G. R. Sell, Robustness of the exponential dichotomy in infinite-dimensional dynamical systems, J. Dynam. Differential Equations, 11 (1999), 471-513.
doi: 10.1023/A:1021913903923. |
[23] |
R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems, III, J. Differential Equations, 22 (1976), 497-522.
doi: 10.1016/0022-0396(76)90043-7. |
[24] |
B. Sasu and A. L. Sasu, Exponential dichotomy and $(l^p, l^q)$-admissibility on the half-line, J. Math. Anal. Appl., 316 (2006), 397-408.
doi: 10.1016/j.jmaa.2005.04.047. |
[25] |
B. Sasu, Uniform dichotomy and exponential dichotomy of evolution families on the half-line, J. Math. Anal. Appl., 323 (2006), 1465-1478.
doi: 10.1016/j.jmaa.2005.12.002. |
[26] |
B. Sasu and A. L. Sasu, Exponential trichotomy and p-admissibility for evolution families on the real line, Math. Z., 253 (2006), 515-536.
doi: 10.1007/s00209-005-0920-8. |
[27] |
A. L. 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. |
[28] |
A. L. Sasu and B. Sasu, Exponential trichotomy for variational difference equations, J. Difference Equ. Appl., 15 (2009), 693-718.
doi: 10.1080/10236190802285118. |
[29] |
A. L. Sasu and B. Sasu, Input-output admissibility and exponential trichotomy of difference equations, J. Math. Anal. Appl., 380 (2011), 17-32.
doi: 10.1016/j.jmaa.2011.02.045. |
[30] |
B. Sasu and A. L. Sasu, On the dichotomic behavior of discrete dynamical systems on the half-line, Discrete Contin. Dyn. Syst., 33 (2013), 3057-3084.
doi: 10.3934/dcds.2013.33.3057. |
[31] |
X. Liu, Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium, Appl. Math. Lett., 23 (2010), 409-416.
doi: 10.1016/j.aml.2009.11.008. |
[32] |
D. Zhu, Exponential trichotomy and heteroclinic bifurcations, Nonlinear Anal., 28 (1997), 547-557.
doi: 10.1016/0362-546X(95)00164-Q. |
show all references
References:
[1] |
A. I. Alonso, J. Hong and R. Obaya, Exponential dichotomy and trichotomy for difference equations, Comput. Math. Appl., 38 (1999), 41-49.
doi: 10.1016/S0898-1221(99)00167-4. |
[2] |
L. Barreira and C. Valls, Center manifolds for nonuniformly partially hyperbolic diffeomorphisms, J. Math. Pures Appl. (9), 84 (2005), 1693-1715.
doi: 10.1016/j.matpur.2005.07.005. |
[3] |
L. Barreira and C. Valls, Center manifolds for infinite delay, J. Differential Equations, 247 (2009), 1297-1310.
doi: 10.1016/j.jde.2009.04.006. |
[4] |
L. Barreira and C. Valls, Robustness of nonuniform exponential trichotomies in Banach spaces, J. Math. Anal. Appl., 351 (2009), 373-381.
doi: 10.1016/j.jmaa.2008.10.030. |
[5] |
L. Barreira and C. Valls, Lyapunov functions for trichotomies with growth rates, J. Differential Equations, 248 (2010), 151-183.
doi: 10.1016/j.jde.2009.07.001. |
[6] |
L. Barreira and C. Valls, Nonuniform exponential dichotomies and admissibility, Discrete Contin. Dyn. Syst., 30 (2011), 39-53.
doi: 10.3934/dcds.2011.30.39. |
[7] |
L. Barreira and C. Valls, Admissibility versus nonuniform exponential behavior for noninver-tible cocycles, Discrete Contin. Dyn. Syst., 33 (2013), 1297-1311. |
[8] |
C. V. Coffman and J. J. Schäffer, Dichotomies for linear difference equations, Math. Ann., 172 (1967), 139-166.
doi: 10.1007/BF01350095. |
[9] |
S.-N. Chow and H. Leiva, Existence and roughness of the exponential dichotomy for linear skew-product semiflows in Banach spaces, J. Differential Equations, 120 (1995), 429-477.
doi: 10.1006/jdeq.1995.1117. |
[10] |
Ju. L. Dalec'kiĭ and M. G. Kreĭn, Stability of Solutions of Differential Equations in Banach Spaces, Trans. Math. Monographs, Vol. 43, Amer. Math. Soc., Providence R.I., 1974. |
[11] |
S. Elaydi and O. Hájek, Some remarks on nonlinear dichotomy and trichotomy, in Non-linear Analysis and Applications (Arlington, Tex., 1986), Lect. Notes Pure Appl. Math., 109, Dekker, New York, (1987), 175-178. |
[12] |
S. Elaydi and O. Hájek, Exponential trichotomy of differential systems, J. Math. Anal. Appl., 129 (1988), 362-374.
doi: 10.1016/0022-247X(88)90255-7. |
[13] |
S. Elaydi and O. Hájek, Exponential dichotomy and trichotomy of nonlinear differential equations, Differ. Integral Equ., 3 (1990), 1201-1224. |
[14] |
S. Elaydi and K. Janglajew, Dichotomy and trichotomy of difference equations, J. Differ. Equations Appl., 3 (1998), 417-448.
doi: 10.1080/10236199708808113. |
[15] |
N. T. Huy and N. Van Minh, Exponential dichotomy of difference equations and applications to evolution equations on the half-line, Comput. Math. Appl., 42 (2001), 301-311.
doi: 10.1016/S0898-1221(01)00155-9. |
[16] |
J. López-Fenner and M. Pinto, $(h,k)$-trichotomies and asymptotics of nonautonomous difference equations, Comp. Math. Appl., 33 (1997), 105-124.
doi: 10.1016/S0898-1221(97)00080-1. |
[17] |
J. L. Massera and J. J. Schäffer, Linear Differential Equations and Function Spaces, Pure and Applied Mathematics, Vol. 21, Academic Press, New York-London, 1966. |
[18] |
M. Megan, A. L. Sasu and B. Sasu, Discrete admissibility and exponential dichotomy for evolution families, Discrete Contin. Dyn. Syst., 9 (2003), 383-397. |
[19] |
N. Van Minh and N. T. 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. |
[20] |
O. Perron, Die Stabilitätsfrage bei Differentialgleischungen, Math. Z., 32 (1930), 703-728.
doi: 10.1007/BF01194662. |
[21] |
K. J. Palmer, Exponential dichotomy and expansivity, Ann. Mat. Pura Appl. (4), 185 (2006), S171-S185.
doi: 10.1007/s10231-004-0141-5. |
[22] |
V. A. Pliss and G. R. Sell, Robustness of the exponential dichotomy in infinite-dimensional dynamical systems, J. Dynam. Differential Equations, 11 (1999), 471-513.
doi: 10.1023/A:1021913903923. |
[23] |
R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems, III, J. Differential Equations, 22 (1976), 497-522.
doi: 10.1016/0022-0396(76)90043-7. |
[24] |
B. Sasu and A. L. Sasu, Exponential dichotomy and $(l^p, l^q)$-admissibility on the half-line, J. Math. Anal. Appl., 316 (2006), 397-408.
doi: 10.1016/j.jmaa.2005.04.047. |
[25] |
B. Sasu, Uniform dichotomy and exponential dichotomy of evolution families on the half-line, J. Math. Anal. Appl., 323 (2006), 1465-1478.
doi: 10.1016/j.jmaa.2005.12.002. |
[26] |
B. Sasu and A. L. Sasu, Exponential trichotomy and p-admissibility for evolution families on the real line, Math. Z., 253 (2006), 515-536.
doi: 10.1007/s00209-005-0920-8. |
[27] |
A. L. 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. |
[28] |
A. L. Sasu and B. Sasu, Exponential trichotomy for variational difference equations, J. Difference Equ. Appl., 15 (2009), 693-718.
doi: 10.1080/10236190802285118. |
[29] |
A. L. Sasu and B. Sasu, Input-output admissibility and exponential trichotomy of difference equations, J. Math. Anal. Appl., 380 (2011), 17-32.
doi: 10.1016/j.jmaa.2011.02.045. |
[30] |
B. Sasu and A. L. Sasu, On the dichotomic behavior of discrete dynamical systems on the half-line, Discrete Contin. Dyn. Syst., 33 (2013), 3057-3084.
doi: 10.3934/dcds.2013.33.3057. |
[31] |
X. Liu, Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium, Appl. Math. Lett., 23 (2010), 409-416.
doi: 10.1016/j.aml.2009.11.008. |
[32] |
D. Zhu, Exponential trichotomy and heteroclinic bifurcations, Nonlinear Anal., 28 (1997), 547-557.
doi: 10.1016/0362-546X(95)00164-Q. |
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