References
- Datko R. Extending a theorem of A. M. Liapunov to Hilbert space. J Math Anal Appl. 1970;32:610–616. doi: https://doi.org/10.1016/0022-247X(70)90283-0
- Pazy A. On the applicability of Lyapunov's theorem in Hilbert space. SIAM J Math Anal. 1972;3:291–294. doi: https://doi.org/10.1137/0503028
- Zabczyk J. Remarks on the control of discrete-time distributed parameter systems. SIAM J Control Optim. 1974;12:721–735. doi: https://doi.org/10.1137/0312056
- Kellett CM. Classical converse theorems in Lyapunov's second method. Discrete Contin Dyn Syst B. 2015;20:2333–2360. doi: https://doi.org/10.3934/dcdsb.2015.20.2333
- Datko R. Uniform asymptotic stability of evolutionary processes in Banach space. SIAM J Math Anal. 1972;3:428–445. doi: https://doi.org/10.1137/0503042
- Rolewicz S. On uniform N-equistability. J Math Anal Appl. 1986;115:434–441. doi: https://doi.org/10.1016/0022-247X(86)90006-5
- Przyluski KM, Rolewicz S. On stability of linear time-varying infinite-dimensional discrete-time systems. Syst Control Lett. 1984;4:307–315. doi: https://doi.org/10.1016/S0167-6911(84)80042-0
- Storozhuk KV. On the Rolewicz theorem for evolution families. Proc Am Math Soc. 2007;135:1861–1863. doi: https://doi.org/10.1090/S0002-9939-07-08697-2
- Bento A, Lupa N, Megan M, et al. Integral conditions for nonuniform μ-dichotomy on the half-line. Discrete Contin Dyn Syst Ser B. 2017;22:3063–3077.
- Buse C, Dragomir S. New characterizations of asymptotic stability for evolution families on Banach spaces. Electron J Differ Equ. 2004;38:9pp.
- Dragičević D. Strong nonuniform behaviour: a Datko type characterization. J Math Anal Appl. 2018;459:266–290. doi: https://doi.org/10.1016/j.jmaa.2017.10.056
- Haak B, van Neerven J, Veraar M. A stochastic Datko-Pazy theorem. J Math Anal Appl. 2007;329:1230–1239. doi: https://doi.org/10.1016/j.jmaa.2006.07.051
- Lupa N, Popescu LH. Banach function spaces and Datko-type conditions for nonuniform exponential stability of evolution families.
- Megan M, Sasu B, Sasu AL. On uniform exponential stability of evolution families. Riv Mat Univ Parma. 2001;4:27–43.
- Moşincat RO, Preda C, Preda P. Averaging theorems for the large-time behavior of the solutions of nonautonomous systems. Syst Control Lett. 2011;60:994–999. doi: https://doi.org/10.1016/j.sysconle.2011.08.003
- Preda C, Preda P, Craciunescu A. A version of a theorem of R. Datko for nonuniform exponential contractions. J Math Anal Appl. 2012;385:572–581. doi: https://doi.org/10.1016/j.jmaa.2011.06.082
- Sasu AL, Megan M, Sasu B. On Rolewicz-Zabczyk techniques in the stability theory of dynamical systems. Fixed Point Theory. 2012;13:205–236.
- Megan M, Sasu AL, Sasu B. On uniform exponential stability of linear skew-product semiflows in Banach spaces. Bull Belg Math Soc Simon Stevin. 2002;9:143–154.
- Preda C, Preda P, Petre A. On the asymptotic behavior of an exponentially bounded, strongly continuous cocycle over a semiflow. Commun Pure Appl Anal. 2009;8:1637–1645. doi: https://doi.org/10.3934/cpaa.2009.8.1637
- Sasu AL, Sasu B. Exponential stability for linear skew-product flows. Bull Sci Math. 2004;128:727–738. doi: https://doi.org/10.1016/j.bulsci.2004.03.010
- Sasu B. Generalizations of a theorem of Rolewicz. Appl Anal. 2005;84:1165–1172. doi: https://doi.org/10.1080/00036810410001724391
- Sasu B. On exponential dichotomy of variational difference equations. Discrete Dyn Nat Soc. 2009;2009:324273, 18pp.
- Sasu B. Integral conditions for exponential dichotomy: a nonlinear approach. Bull Sci Math. 2010;134:235–246. doi: https://doi.org/10.1016/j.bulsci.2009.06.006
- Dragičević D. A version of a theorem of R. Datko for stability in average. Syst Control Lett. 2016;96:1–6. doi: https://doi.org/10.1016/j.sysconle.2016.06.015
- Barreira L, Pesin Ya. Nonuniform hyperbolicity. Cambridge: Cambridge University Press; 2007.
- Chicone C, Latushkin Yu. Evolution semigroups in dynamical systems and differential equations. Providence (RI): American Mathematical Society; 1999. (Mathematical Surveys and Monographs, Vol. 70).
- Arnold L. Random dynamical systems. Berlin: Springer; 1998. (Springer Monographs in Mathematics).
- Dragičević D. Datko-Pazy conditions for nonuniform exponential stability. J Differ Equ Appl. 2018;24:344–357. doi: https://doi.org/10.1080/10236198.2017.1408609
- Preda C, Preda P, Bǎtǎran F. An extension of a theorem of R. Datko to the case of (non)uniform exponential stability of linear skew-product semiflows. J Math Anal Appl. 2015;425:1148–1154. doi: https://doi.org/10.1016/j.jmaa.2015.01.014
- Preda C, Onofrei OR. Nonuniform exponential dichotomy for linear skew-product semiflows over semiflows. Semigroup Forum. 2018;96:241–252. doi: https://doi.org/10.1007/s00233-017-9868-3
- Morris ID. Mather sets for sequences of matrices and applications to the study of joint spectral radii. Proc Lond Math Soc. 2013;107:121–150. doi: https://doi.org/10.1112/plms/pds080
- Cao Y. On growth rates of sub-additive functions for semi-flows: determined and random cases. J Differ Equ. 2006;231:1–17. doi: https://doi.org/10.1016/j.jde.2006.08.016
- Schreiber SJ. On growth rates of subadditive functions for semiflows. J Differ Equ. 1998;148:334–350. doi: https://doi.org/10.1006/jdeq.1998.3471
- Sturman R, Stark J. Semi-uniform ergodic theorems and applications to forced systems. Nonlinearity. 2000;13:113–145. doi: https://doi.org/10.1088/0951-7715/13/1/306
- Oseledets V. A multiplicative ergodic theorem. Liapunov characteristic numbers for dynamical systems. Trans Moscow Math Soc. 1968;19:197–221.
- Pesin JB. Families of invariant manifolds corresponding to nonzero characteristic exponents. Math USSR-Izv. 1976;10:1261–1305. doi: https://doi.org/10.1070/IM1976v010n06ABEH001835
- Pesin Ya. Characteristic Ljapunov exponents, and smooth ergodic theory. Russian Math Surveys. 1977;32:55–114. doi: https://doi.org/10.1070/RM1977v032n04ABEH001639
- Smale S. Differentiable dynamical systems. Bull Am Math Soc. 1967;73:747–817. doi: https://doi.org/10.1090/S0002-9904-1967-11798-1
- González-Tokman C, Quas A. A semi-invertible operator Oseledets theorem. Ergodic Theory Dyn Syst. 2014;34:1230–1272. doi: https://doi.org/10.1017/etds.2012.189
- Kingman JFC. Sub-additive ergodic theory. Ann Probab. 1973;1:883–899. doi: https://doi.org/10.1214/aop/1176996798
- Viana M, Oliveira K. Foundations of ergodic theory. 2016. Cambridge: Cambridge University Press (Cambridge Studies in Advanced Mathematics).
- Walters P. An introduction to ergodic theory. Berlin: Springer; 1981.
- Barreira L, Schmeling J. Sets of ‘non-typical’ points have full topological entropy and full Hausdorff dimension. Israel J Math. 2000;116:29–70. doi: https://doi.org/10.1007/BF02773211
- Blumenthal A, Young LS. Entropy, volume growth and SRB measures for Banach space mappings. Invent Math. 2017;207:833–893. doi: https://doi.org/10.1007/s00222-016-0678-0
- Froyland G, Lloyd S, Quas A. A semi-invertible Oseledets theorem with applications to transfer operator cocycles. Discrete Contin Dyn Syst. 2013;33:3835–3860. doi: https://doi.org/10.3934/dcds.2013.33.3835
- van Neerven JMAM. Lower semicontinuity and the theorem of Datko and Pazy. Integr Equ Oper Theory. 2002;42:482–492. doi: https://doi.org/10.1007/BF01270925
- Barreira L, Dragičević D, Valls C, Tempered exponential dichotomies: admissibility and stability under perturbations. Dyn Syst. 2016;31:525–545. doi: https://doi.org/10.1080/14689367.2016.1159663
- Zhou L, Lu K, Zhang W. Roughness of tempered dichotomies for infinite-dimensional random difference equations. J Differ Equ. 2012;254:4024–4046. doi: https://doi.org/10.1016/j.jde.2013.02.007
- Barreira L, Dragičević D, Valls C. Admissibility and nonuniformly hyperbolic sets. Electron J Qual Theory Differ Equ. 2016;10:1–15.