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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.
|
[2] |
L. Barreira, D. Dragičević and C. Valls, Admissibility in the strong and weak senses,, preprint., (). Google Scholar |
[3] |
L. Barreira and Ya. Pesin, Lyapunov Exponents and Smooth Ergodic Theory,, University Lecture Series, (2002).
|
[4] |
L. Barreira and Ya. Pesin, Nonuniform Hyperbolicity,, Encyclopedia of Mathematics and its Applications, (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.
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.
doi: 10.1007/s10884-006-9026-1. |
[7] |
L. Barreira and C. Valls, Stability theory and Lyapunov regularity,, J. Differential Equations, 232 (2007), 675.
doi: 10.1016/j.jde.2006.09.021. |
[8] |
L. Barreira and C. Valls, Stability of Nonautonomous Differential Equations,, Lect. Notes in Math., (1926).
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.
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, (1999).
doi: 10.1090/surv/070. |
[11] |
C. Coffman and J. Schäffer, Dichotomies for linear difference equations,, Math. Ann., 172 (1967), 139.
doi: 10.1007/BF01350095. |
[12] |
W. Coppel, On the stability of ordinary differential equations,, J. London Math. Soc., 39 (1964), 255.
|
[13] |
W. Coppel, Dichotomies in Stability Theory,, Lect. Notes. in Math., (1978).
|
[14] |
Ju. Dalec$'$kiĭ and M. Kreĭn, Stability of Solutions of Differential Equations in Banach Space,, Translations of Mathematical Monographs, (1974).
|
[15] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations,, Lect. Notes in Math., (1981).
|
[16] |
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. |
[17] |
N. Huy and N. Ha, Exponential dichotomy of difference equations in $l_p$-phase spaces on the half-line,, Adv. Difference Equ., (2006).
|
[18] |
Yu. Latushkin, A. Pogan and R. Schnaubelt, Dichotomy and Fredholm properties of evolution equations,, J. Operator Theory, 58 (2007), 387.
|
[19] |
Yu. Latushkin and Yu. Tomilov, Fredholm differential operators with unbounded coefficients,, J. Differential Equations, 208 (2005), 388.
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.
doi: 10.1007/BF02547352. |
[22] |
A. Maizel', On stability of solutions of systems of differential equations,, Trudi Ural'skogo Politekhnicheskogo Instituta, 51 (1954), 20.
|
[23] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I,, Ann. of Math. (2), 67 (1958), 517.
doi: 10.2307/1969871. |
[24] |
J. Massera and J. Schäffer, Linear Differential Equations and Function Spaces,, Pure and Applied Mathematics, (1966).
|
[25] |
K. Palmer, Exponential dichotomies and transversal homoclinic points,, J. Differential Equations, 55 (1984), 225.
doi: 10.1016/0022-0396(84)90082-2. |
[26] |
K. Palmer, Exponential dichotomies and Fredholm operators,, Proc. Amer. Math. Soc., 104 (1988), 149.
doi: 10.1090/S0002-9939-1988-0958058-1. |
[27] |
O. Perron, Die Stabilitätsfrage bei Differentialgleichungen,, Math. Z., 32 (1930), 703.
doi: 10.1007/BF01194662. |
[28] |
Ya. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents,, Math. USSR-Izv., 10 (1976), 1261.
|
[29] |
Ya. Pesin, Characteristic Ljapunov exponents, and smooth ergodic theory,, Russian Math. Surveys, 32 (1977), 55.
|
[30] |
S. Pilyugin, Generalizations of the notion of hyperbolicity,, J. Difference Equ. Appl., 12 (2006), 271.
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, (1977), 168.
|
[32] |
R. Sacker and G. Sell, A spectral theory for linear differential systems,, J. Differential Equations, 27 (1978), 320.
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.
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.
|
[2] |
L. Barreira, D. Dragičević and C. Valls, Admissibility in the strong and weak senses,, preprint., (). Google Scholar |
[3] |
L. Barreira and Ya. Pesin, Lyapunov Exponents and Smooth Ergodic Theory,, University Lecture Series, (2002).
|
[4] |
L. Barreira and Ya. Pesin, Nonuniform Hyperbolicity,, Encyclopedia of Mathematics and its Applications, (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.
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.
doi: 10.1007/s10884-006-9026-1. |
[7] |
L. Barreira and C. Valls, Stability theory and Lyapunov regularity,, J. Differential Equations, 232 (2007), 675.
doi: 10.1016/j.jde.2006.09.021. |
[8] |
L. Barreira and C. Valls, Stability of Nonautonomous Differential Equations,, Lect. Notes in Math., (1926).
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.
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, (1999).
doi: 10.1090/surv/070. |
[11] |
C. Coffman and J. Schäffer, Dichotomies for linear difference equations,, Math. Ann., 172 (1967), 139.
doi: 10.1007/BF01350095. |
[12] |
W. Coppel, On the stability of ordinary differential equations,, J. London Math. Soc., 39 (1964), 255.
|
[13] |
W. Coppel, Dichotomies in Stability Theory,, Lect. Notes. in Math., (1978).
|
[14] |
Ju. Dalec$'$kiĭ and M. Kreĭn, Stability of Solutions of Differential Equations in Banach Space,, Translations of Mathematical Monographs, (1974).
|
[15] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations,, Lect. Notes in Math., (1981).
|
[16] |
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. |
[17] |
N. Huy and N. Ha, Exponential dichotomy of difference equations in $l_p$-phase spaces on the half-line,, Adv. Difference Equ., (2006).
|
[18] |
Yu. Latushkin, A. Pogan and R. Schnaubelt, Dichotomy and Fredholm properties of evolution equations,, J. Operator Theory, 58 (2007), 387.
|
[19] |
Yu. Latushkin and Yu. Tomilov, Fredholm differential operators with unbounded coefficients,, J. Differential Equations, 208 (2005), 388.
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.
doi: 10.1007/BF02547352. |
[22] |
A. Maizel', On stability of solutions of systems of differential equations,, Trudi Ural'skogo Politekhnicheskogo Instituta, 51 (1954), 20.
|
[23] |
J. Massera and J. Schäffer, Linear differential equations and functional analysis. I,, Ann. of Math. (2), 67 (1958), 517.
doi: 10.2307/1969871. |
[24] |
J. Massera and J. Schäffer, Linear Differential Equations and Function Spaces,, Pure and Applied Mathematics, (1966).
|
[25] |
K. Palmer, Exponential dichotomies and transversal homoclinic points,, J. Differential Equations, 55 (1984), 225.
doi: 10.1016/0022-0396(84)90082-2. |
[26] |
K. Palmer, Exponential dichotomies and Fredholm operators,, Proc. Amer. Math. Soc., 104 (1988), 149.
doi: 10.1090/S0002-9939-1988-0958058-1. |
[27] |
O. Perron, Die Stabilitätsfrage bei Differentialgleichungen,, Math. Z., 32 (1930), 703.
doi: 10.1007/BF01194662. |
[28] |
Ya. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents,, Math. USSR-Izv., 10 (1976), 1261.
|
[29] |
Ya. Pesin, Characteristic Ljapunov exponents, and smooth ergodic theory,, Russian Math. Surveys, 32 (1977), 55.
|
[30] |
S. Pilyugin, Generalizations of the notion of hyperbolicity,, J. Difference Equ. Appl., 12 (2006), 271.
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, (1977), 168.
|
[32] |
R. Sacker and G. Sell, A spectral theory for linear differential systems,, J. Differential Equations, 27 (1978), 320.
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.
doi: 10.3934/dcds.2013.33.4187. |
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