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On the asymptotics of the scenery flow
From one-sided dichotomies to two-sided dichotomies
1. | Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa |
2. | Department of Mathematics, University of Rijeka, 51000 Rijeka, Croatia |
References:
[1] |
L. Barreira, D. Dragičević and C. Valls, Nonuniform hyperbolicity and admissibility, Adv. Nonlinear Stud., 14 (2014), 791-811. |
[2] |
L. Barreira, D. Dragičević and C. Valls, Admissibility in the strong and weak senses,, preprint., ().
|
[3] |
L. Barreira and Ya. Pesin, Lyapunov Exponents and Smooth Ergodic Theory, University Lecture Series, 23, Amer. Math. Soc., 2002. |
[4] |
L. Barreira and Ya. Pesin, Nonuniform Hyperbolicity, Encyclopedia of Mathematics and its Applications, 115, Cambridge University Press, 2007.
doi: 10.1017/CBO9781107326026. |
[5] |
L. Barreira and C. Valls, A Grobman-Hartman theorem for nonuniformly hyperbolic dynamics, J. Differential Equations, 228 (2006), 285-310.
doi: 10.1016/j.jde.2006.04.001. |
[6] |
L. Barreira and C. Valls, Nonuniform exponential dichotomies and Lyapunov regularity, J. Dynam. Differential Equations, 19 (2007), 215-241.
doi: 10.1007/s10884-006-9026-1. |
[7] |
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. |
[8] |
L. Barreira and C. Valls, Stability of Nonautonomous Differential Equations, Lect. Notes in Math., 1926, Springer, 2008.
doi: 10.1007/978-3-540-74775-8. |
[9] |
L. Barreira and C. Valls, Lyapunov sequences for exponential dichotomies, J. Differential Equations, 246 (2009), 183-215.
doi: 10.1016/j.jde.2008.06.009. |
[10] |
C. Chicone and Yu. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Mathematical Surveys and Monographs, 70, Amer. Math. Soc., 1999.
doi: 10.1090/surv/070. |
[11] |
C. Coffman and J. Schäffer, Dichotomies for linear difference equations, Math. Ann., 172 (1967), 139-166.
doi: 10.1007/BF01350095. |
[12] |
W. Coppel, On the stability of ordinary differential equations, J. London Math. Soc., 39 (1964), 255-260. |
[13] |
W. Coppel, Dichotomies in Stability Theory, Lect. Notes. in Math., 629, Springer, 1978. |
[14] |
Ju. Dalec$'$kiĭ and M. Kreĭn, Stability of Solutions of Differential Equations in Banach Space, Translations of Mathematical Monographs, 43, Amer. Math. Soc., 1974. |
[15] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lect. Notes in Math., 840, Springer, 1981. |
[16] |
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. |
[17] |
N. Huy and N. Ha, Exponential dichotomy of difference equations in $l_p$-phase spaces on the half-line, Adv. Difference Equ., 2006, Art. ID 58453, 14 pp. |
[18] |
Yu. Latushkin, A. Pogan and R. Schnaubelt, Dichotomy and Fredholm properties of evolution equations, J. Operator Theory, 58 (2007), 387-414. |
[19] |
Yu. Latushkin and Yu. Tomilov, Fredholm differential operators with unbounded coefficients, J. Differential Equations, 208 (2005), 388-429.
doi: 10.1016/j.jde.2003.10.018. |
[20] |
B. Levitan and V. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge University Press, 1982. |
[21] |
T. Li, Die Stabilitätsfrage bei Differenzengleichungen, Acta Math., 63 (1934), 99-141.
doi: 10.1007/BF02547352. |
[22] |
A. Maizel', On stability of solutions of systems of differential equations, Trudi Ural'skogo Politekhnicheskogo Instituta, Mathematics, 51 (1954), 20-50. |
[23] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I, Ann. of Math. (2), 67 (1958), 517-573.
doi: 10.2307/1969871. |
[24] |
J. Massera and J. Schäffer, Linear Differential Equations and Function Spaces, Pure and Applied Mathematics, 21, Academic Press, 1966. |
[25] |
K. Palmer, Exponential dichotomies and transversal homoclinic points, J. Differential Equations, 55 (1984), 225-256.
doi: 10.1016/0022-0396(84)90082-2. |
[26] |
K. Palmer, Exponential dichotomies and Fredholm operators, Proc. Amer. Math. Soc., 104 (1988), 149-156.
doi: 10.1090/S0002-9939-1988-0958058-1. |
[27] |
O. Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z., 32 (1930), 703-728.
doi: 10.1007/BF01194662. |
[28] |
Ya. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents, Math. USSR-Izv., 10 (1976), 1261-1305. |
[29] |
Ya. Pesin, Characteristic Ljapunov exponents, and smooth ergodic theory, Russian Math. Surveys, 32 (1977), 55-114. |
[30] |
S. Pilyugin, Generalizations of the notion of hyperbolicity, J. Difference Equ. Appl., 12 (2006), 271-282.
doi: 10.1080/10236190500489350. |
[31] |
V. Pliss, Bounded solutions of inhomogeneous linear systems of differential equations (in Russian), in Problems of Asymptotic Theory of Nonlinear Oscillations, Naukova Dumka, Kiev, 1977, 168-173. |
[32] |
R. Sacker and G. Sell, A spectral theory for linear differential systems, J. Differential Equations, 27 (1978), 320-358.
doi: 10.1016/0022-0396(78)90057-8. |
[33] |
D. Todorov, Generalizations of analogs of theorems of Maizel and Pliss and their application in shadowing theory, Discrete Contin. Dyn. Syst., 33 (2013), 4187-4205.
doi: 10.3934/dcds.2013.33.4187. |
show all references
References:
[1] |
L. Barreira, D. Dragičević and C. Valls, Nonuniform hyperbolicity and admissibility, Adv. Nonlinear Stud., 14 (2014), 791-811. |
[2] |
L. Barreira, D. Dragičević and C. Valls, Admissibility in the strong and weak senses,, preprint., ().
|
[3] |
L. Barreira and Ya. Pesin, Lyapunov Exponents and Smooth Ergodic Theory, University Lecture Series, 23, Amer. Math. Soc., 2002. |
[4] |
L. Barreira and Ya. Pesin, Nonuniform Hyperbolicity, Encyclopedia of Mathematics and its Applications, 115, Cambridge University Press, 2007.
doi: 10.1017/CBO9781107326026. |
[5] |
L. Barreira and C. Valls, A Grobman-Hartman theorem for nonuniformly hyperbolic dynamics, J. Differential Equations, 228 (2006), 285-310.
doi: 10.1016/j.jde.2006.04.001. |
[6] |
L. Barreira and C. Valls, Nonuniform exponential dichotomies and Lyapunov regularity, J. Dynam. Differential Equations, 19 (2007), 215-241.
doi: 10.1007/s10884-006-9026-1. |
[7] |
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. |
[8] |
L. Barreira and C. Valls, Stability of Nonautonomous Differential Equations, Lect. Notes in Math., 1926, Springer, 2008.
doi: 10.1007/978-3-540-74775-8. |
[9] |
L. Barreira and C. Valls, Lyapunov sequences for exponential dichotomies, J. Differential Equations, 246 (2009), 183-215.
doi: 10.1016/j.jde.2008.06.009. |
[10] |
C. Chicone and Yu. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Mathematical Surveys and Monographs, 70, Amer. Math. Soc., 1999.
doi: 10.1090/surv/070. |
[11] |
C. Coffman and J. Schäffer, Dichotomies for linear difference equations, Math. Ann., 172 (1967), 139-166.
doi: 10.1007/BF01350095. |
[12] |
W. Coppel, On the stability of ordinary differential equations, J. London Math. Soc., 39 (1964), 255-260. |
[13] |
W. Coppel, Dichotomies in Stability Theory, Lect. Notes. in Math., 629, Springer, 1978. |
[14] |
Ju. Dalec$'$kiĭ and M. Kreĭn, Stability of Solutions of Differential Equations in Banach Space, Translations of Mathematical Monographs, 43, Amer. Math. Soc., 1974. |
[15] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lect. Notes in Math., 840, Springer, 1981. |
[16] |
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. |
[17] |
N. Huy and N. Ha, Exponential dichotomy of difference equations in $l_p$-phase spaces on the half-line, Adv. Difference Equ., 2006, Art. ID 58453, 14 pp. |
[18] |
Yu. Latushkin, A. Pogan and R. Schnaubelt, Dichotomy and Fredholm properties of evolution equations, J. Operator Theory, 58 (2007), 387-414. |
[19] |
Yu. Latushkin and Yu. Tomilov, Fredholm differential operators with unbounded coefficients, J. Differential Equations, 208 (2005), 388-429.
doi: 10.1016/j.jde.2003.10.018. |
[20] |
B. Levitan and V. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge University Press, 1982. |
[21] |
T. Li, Die Stabilitätsfrage bei Differenzengleichungen, Acta Math., 63 (1934), 99-141.
doi: 10.1007/BF02547352. |
[22] |
A. Maizel', On stability of solutions of systems of differential equations, Trudi Ural'skogo Politekhnicheskogo Instituta, Mathematics, 51 (1954), 20-50. |
[23] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I, Ann. of Math. (2), 67 (1958), 517-573.
doi: 10.2307/1969871. |
[24] |
J. Massera and J. Schäffer, Linear Differential Equations and Function Spaces, Pure and Applied Mathematics, 21, Academic Press, 1966. |
[25] |
K. Palmer, Exponential dichotomies and transversal homoclinic points, J. Differential Equations, 55 (1984), 225-256.
doi: 10.1016/0022-0396(84)90082-2. |
[26] |
K. Palmer, Exponential dichotomies and Fredholm operators, Proc. Amer. Math. Soc., 104 (1988), 149-156.
doi: 10.1090/S0002-9939-1988-0958058-1. |
[27] |
O. Perron, Die Stabilitätsfrage bei Differentialgleichungen, Math. Z., 32 (1930), 703-728.
doi: 10.1007/BF01194662. |
[28] |
Ya. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents, Math. USSR-Izv., 10 (1976), 1261-1305. |
[29] |
Ya. Pesin, Characteristic Ljapunov exponents, and smooth ergodic theory, Russian Math. Surveys, 32 (1977), 55-114. |
[30] |
S. Pilyugin, Generalizations of the notion of hyperbolicity, J. Difference Equ. Appl., 12 (2006), 271-282.
doi: 10.1080/10236190500489350. |
[31] |
V. Pliss, Bounded solutions of inhomogeneous linear systems of differential equations (in Russian), in Problems of Asymptotic Theory of Nonlinear Oscillations, Naukova Dumka, Kiev, 1977, 168-173. |
[32] |
R. Sacker and G. Sell, A spectral theory for linear differential systems, J. Differential Equations, 27 (1978), 320-358.
doi: 10.1016/0022-0396(78)90057-8. |
[33] |
D. Todorov, Generalizations of analogs of theorems of Maizel and Pliss and their application in shadowing theory, Discrete Contin. Dyn. Syst., 33 (2013), 4187-4205.
doi: 10.3934/dcds.2013.33.4187. |
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