\((h,k)\)-trichotomies and asymptotics of nonautonomous difference systems

DOI10.1016/S0898-1221(97)00080-1zbMath0880.39012OpenAlexW2091311901MaRDI QIDQ1368828

Julio López Fenner, Manuel Pinto

Publication date: 8 February 1998

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(97)00080-1

zbMATH Keywords

invariant manifoldasymptotic equivalencetrichotomiesdifference systemsdiscrete nonautonomous nonlinear systems

Mathematics Subject Classification ID

Related Items (15)

\((h,k)\)-trichotomies and asymptotics of nonautonomous difference systems ⋮ Dichotomy and existence of periodic solutions of quasilinear functional differential equations ⋮ Admissibility and exponential trichotomy of dynamical systems described by skew-product flows ⋮ Discrete admissibility and exponential trichotomy of dynamical systems ⋮ Nonuniform exponential trichotomy for linear discrete-time systems in Banach spaces ⋮ Weighted convergent and bounded solutions of difference systems ⋮ The equivalence of Datko and Lyapunov properties for \((h, k)\)-trichotomic linear discrete-time systems ⋮ Discrete \((h,k)\)-dichotomy and remarks on the boundedness of the projections ⋮ Lyapunov type equation for discrete exponential trichotomies ⋮ Linear attraction in quasi-linear difference systems ⋮ Existence and roughness of nonuniform \((h,k,\mu,\nu)\)-trichotomy for nonautonomous differential equations ⋮ Input-output admissibility and exponential trichotomy of difference equations ⋮ Nonlinear criteria for the existence of the exponential trichotomy in infinite dimensional spaces ⋮ Error estimates for approximating non-hyperbolic heteroclinic orbits of maps ⋮ Invariant manifolds with asymptotic phase for nonautonomous difference equations

Cites Work

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• Exponential dichotomy and trichotomy of nonlinear differential equations
• Continuous and discrete dynamics near manifolds of equilibria
• On linearly perturbed linear systems
• Asymptotic integration of a system resulting from the perturbation of an h-system
• Behavior of solutions near manifolds of periodic solutions
• Geometric theory of semilinear parabolic equations
• Dichotomies in stability theory
• Discrete dichotomies
• \((h,k)\)-trichotomies and asymptotics of nonautonomous difference systems
• Roughness of \((h,k)\)-dichotomies
• Invariant manifolds with asymptotic phase

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