Lyapunov functions for trichotomies with growth rates

DOI10.1016/j.jde.2009.07.001zbMath1197.34094OpenAlexW1995459866MaRDI QIDQ1046481

Luis Barreira, Claudia Valls

Publication date: 22 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.jde.2009.07.001

zbMATH Keywords

Lyapunov functionsnonuniform exponential trichotomy

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items

Connections between some concepts of polynomial trichotomy for noninvertible evolution operators in Banach spaces, Discrete admissibility and exponential trichotomy of dynamical systems, The equivalence of Datko and Lyapunov properties for \((h, k)\)-trichotomic linear discrete-time systems, Asymptotically almost periodic solutions for a class of stochastic functional differential equations, Lyapunov function and exponential trichotomy on time scales, Existence and roughness of nonuniform \((h,k,\mu,\nu)\)-trichotomy for nonautonomous differential equations, Characterization of tempered exponential dichotomies, On nonuniform polynomial trichotomy of linear discrete-time systems in Banach spaces

Cites Work

• Polynomial growth rates
• Growth rates and nonuniform hyperbolicity
• A reduction principle for nonautonomous systems in infinite-dimensional spaces
• Center manifolds and contractions on a scale of Banach spaces
• Exponential trichotomy of differential systems
• Geometric theory of semilinear parabolic equations
• Existence of dichotomies and invariant splittings for linear differential systems. I
• Existence of dichotomies and invariant splittings for linear differential systems. III
• Dichotomies in stability theory
• Robustness of exponential dichotomies in infinite-dimensional dynamical systems
• Center manifolds for infinite dimensional nonautonomous differential equations
• Center manifolds for invariant sets
• Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces
• Stability of nonautonomous differential equations
• Asymptotic stability without uniform stability: Almost periodic coefficients
• Dichotomies and reducibility
• The stable, center-stable, center, center-unstable, unstable manifolds
• Linear differential equations and functional analysis. I
• Stability of nonautonomous differential equations in Hilbert spaces
• Exponential dichotomy roughness on Banach spaces
• PARTIALLY HYPERBOLIC DYNAMICAL SYSTEMS
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• Admissible perturbations of exponential dichotomy roughness
• Center manifolds for smooth invariant manifolds
• Dynamics of evolutionary equations
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