Evolution semigroups, translation algebras, and exponential dichotomy of cocycles

DOI10.1006/jdeq.1999.3668zbMath0962.34035OpenAlexW2039839603MaRDI QIDQ1970027

Roland Schnaubelt, Yuri Latushkin

Publication date: 29 May 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3668

zbMATH Keywords

evolution semigrouphyperbolicitycocycledichotomyspectral mapping theoremtranslation algebras

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Nonlinear differential equations in abstract spaces (34G20) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items (26)

Existence and robustness of exponential dichotomy of linear skew-product semiflows over semiflows ⋮ Exponential instability of linear skew-product semiflows in terms of Banach function spaces ⋮ Pointwise trichotomy for skew-evolution semiflows on Banach spaces ⋮ Cocycles and Mañe sequences with an application to ideal fluids ⋮ Discrete-time theorems for global and pointwise dichotomies of cocycles over semiflows ⋮ Unnamed Item ⋮ On uniform exponential trisplitting for cocycles of linear operators in Banach spaces ⋮ On uniform polynomial splitting of variational nonautonomous difference equations in Banach spaces ⋮ On spectral characterization of nonuniform hyperbolicity ⋮ Admissibility for nonuniform \((\mu,v)\) contraction and dichotomy ⋮ One admissible critical pair without Lyapunov norm implies a tempered exponential dichotomy for Met-systems ⋮ Perron type theorems for skew-evolution semiflows ⋮ Approaching the discrete dynamical systems by means of skew-evolution semiflows ⋮ Equivalent notions of hyperbolicity ⋮ New conditions for (non)uniform behaviour of linear cocycles over flows ⋮ The essential spectrum of advective equations ⋮ Stability and Stabilizability for Linear Systems of Difference Equations ⋮ Exponential stability for linear skew-product flows ⋮ Schäffer spaces and uniform exponential stability of linear skew-product semiflows ⋮ \((L^p(\mathbb R_+,X),L^q(\mathbb R_+,X))\)-admissibility and exponential dichotomies of cocycles ⋮ THE RELATION BETWEEN THE UNIFORM EXPONENTIAL DICHOTOMY AND THE UNIFORM ADMISSIBILITY OF THE PAIR (l^p, l^q) on ⊝ ⋮ Exponential Expansiveness and Complete Admissibility For Evolution Families ⋮ Discrete and continuous versions of Barbashin-type theorem of linear skew-evolution semiflows ⋮ Discretized characterizations of exponential dichotomy of linear skew-product semiflows over semiflows ⋮ Barbashin-type conditions for exponential stability of linear cocycles ⋮ Criterions for detecting the existence of the exponential dichotomies in the asymptotic behavior of the solutions of variational equations

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