Nonuniform dichotomy spectrum and reducibility for nonautonomous equations

DOI10.1016/j.bulsci.2014.11.002zbMath1344.37038arXiv1402.2067OpenAlexW2024189954MaRDI QIDQ2348249

Yong-Hui Xia, Jifeng Chu, Wei Nian Zhang, Fang-Fang Liao, Stefan Siegmund

Publication date: 11 June 2015

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2067

zbMATH Keywords

reducibilitynonautonomous differential equationsnonuniform exponential dichotomynonuniform dichotomy spectrum

Mathematics Subject Classification ID

Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Topological dynamics of nonautonomous systems (37B55)

Related Items (13)

Does nonuniform behavior destroy the structural stability? ⋮ Dichotomy spectrum and almost topological conjugacy on nonautonomus unbounded difference systems ⋮ Nonuniform \((h,k,\mu,\nu)\)-dichotomy with applications to nonautonomous dynamical systems ⋮ Nonuniform \(\mu \)-dichotomy spectrum and kinematic similarity ⋮ Nonuniform dichotomy spectrum and normal forms for nonautonomous differential systems ⋮ Linearization of a nonautonomous unbounded system with nonuniform contraction: a spectral approach ⋮ The Bohl spectrum for linear nonautonomous differential equations ⋮ Nonuniform dichotomy spectrum and reducibility for nonautonomous difference equations ⋮ NONLINEAR PERTURBATIONS FOR LINEAR NONAUTONOMOUS IMPULSIVE DIFFERENTIAL EQUATIONS AND NONUNIFORM (<i>H,K,µ,ν</i>)-DICHOTOMY ⋮ Nonuniform almost reducibility of nonautonomous linear differential equations ⋮ A new method to prove the nonuniform dichotomy spectrum theorem in ℝⁿ ⋮ NONUNIFORM DICHOTOMY SPECTRUM INTERVALS: THEOREM AND COMPUTATION ⋮ Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Robustness of nonuniform dichotomies with different growth rates
• Robustness of nonuniform behavior for discrete dynamics
• A unified approach to finite-time hyperbolicity which extends finite-time Lyapunov exponents
• Fine structure of the dichotomy spectrum
• Smooth robustness of parameterized perturbations of exponential dichotomies
• Stable manifolds for nonautonomous equations without exponential dichotomy
• On the relationship between exponential dichotomies and the Fredholm alternative
• A spectral theory for linear differential systems
• Dichotomies in stability theory
• On the reducibility of almost periodic systems of linear differential equations
• The concept of spectral dichotomy for linear difference equations
• Dichotomies for linear evolutionary equations in Banach spaces
• Dynamical spectrum for time dependent linear systems in Banach spaces
• Normal forms for nonautonomous differential equations
• Exponential dichotomies and transversal homoclinic points
• The Fredholm alternative and exponential dichotomies for parabolic equation
• Evolutionary semigroups and dichotomy of linear skew-product flows on locally compact spaces with Banach fibers
• Unbounded perturbation of the exponential dichotomy for evolution equations
• Lyapunov functions for general nonuniform dichotomies
• A definition of spectrum for differential equations on finite time
• Stability in nonautonomous dynamics: a survey of recent results
• Transient spectral theory, stable and unstable cones and Gershgorins theorem for finite-time differential equations
• Stability of nonautonomous differential equations
• Dichotomies and reducibility
• Stability of nonautonomous differential equations in Hilbert spaces
• The dichotomy spectrum for noninvertible systems of linear difference equations
• DICHOTOMY SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS
• REDUCIBILITY OF NONAUTONOMOUS LINEAR DIFFERENTIAL EQUATIONS
• The concept of spectral dichotomy for linear difference equations II
• A note on the dichotomy spectrum
• Dichotomy spectrum for nonautonomous differential equations

This page was built for publication: Nonuniform dichotomy spectrum and reducibility for nonautonomous equations