One admissible critical pair without Lyapunov norm implies a tempered exponential dichotomy for Met-systems

DOI10.1142/s0219493723500533OpenAlexW4387405274MaRDI QIDQ6198712

Linfeng Zhou, Wei Nian Zhang, Davor Dragičević

Publication date: 23 February 2024

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493723500533

zbMATH Keywords

random dynamical systemadmissibilitycritical pairtempered exponential dichotomydependence of roughness

Mathematics Subject Classification ID

Dichotomy, trichotomy of solutions to ordinary differential equations (34D09) Dynamical systems and ergodic theory (37-XX) Stability theory for random and stochastic dynamical systems (37H30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonuniform hyperbolicity and one-sided admissibility
• Equivalences between nonuniform exponential dichotomy and admissibility
• Strong and weak \((L^p, L^q)\)-admissibility
• A generalized integral manifold theorem
• Exponential dichotomy and \((\ell^p,\ell^q)\)-admissibility on the half-line
• Admissibility and exponential trichotomy of dynamical systems described by skew-product flows
• Nonuniform behavior and robustness
• Criterions for detecting the existence of the exponential dichotomies in the asymptotic behavior of the solutions of variational equations
• Exponential dichotomies and homoclinic orbits in functional differential equations
• Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system
• Smoothness of spectral subbundles and reducibility of quasi periodic linear differential systems
• Geometric theory of semilinear parabolic equations
• Dichotomies in stability theory
• Exponential dichotomy of difference equations and applications to evolution equations on the half-line
• On spectral characterization of nonuniform hyperbolicity
• Perron conditions for pointwise and global exponential dichotomy of linear skew-product flows
• Discrete admissibility and exponential dichotomy for evolution families
• The Fredholm alternative and exponential dichotomies for parabolic equation
• Evolution equations: Dichotomies and the Fredholm alternative for bounded solutions
• Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces
• Roughness of tempered exponential dichotomies for infinite-dimensional random difference equations
• Evolution semigroups, translation algebras, and exponential dichotomy of cocycles
• On the asymptotic behavior of discrete dynamical systems -- an ergodic theory approach
• Discrete Schäffer spaces and exponential dichotomy for evolution families
• Dichotomies for linear difference equations
• Admissibility and roughness of nonuniform exponential dichotomies for difference equations
• A semi-invertible operator Oseledets theorem
• Smooth robustness of exponential dichotomies
• Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space
• Exponential Dichotomies and Fredholm Operators
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles
• Admissibility and Hyperbolicity
• Exponential dichotomies with respect to a sequence of norms and admissibility
• Tempered exponential dichotomies: admissibility and stability under perturbations
• On the notion of recurrence in discrete stochastic processes

This page was built for publication: One admissible critical pair without Lyapunov norm implies a tempered exponential dichotomy for Met-systems