Spectral theory for linearizations of dynamical systems

DOI10.1016/0022-0396(81)90015-2zbMath0432.58016OpenAlexW2035556143MaRDI QIDQ1138834

Carmen C. Chicone, Richard C. Swanson

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1016/0022-0396(81)90015-2

zbMATH Keywords

centralizers of Anosov vector fieldsflows which are normally hyperbolic at an invariant submanifoldSacker-Sell spectrum of a skew product flowspectrum of linear operators induced on the space of sections by a vector bundle flow

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems with hyperbolic behavior (37D99)

Related Items (14)

The Spectral Characterization of Normal Hyperbolicity ⋮ A note on the fractalization of saddle invariant curves in quasiperiodic systems ⋮ Anosov does not Imply Infinitesimally Ergodic ⋮ Center manifolds for infinite dimensional nonautonomous differential equations ⋮ Lyapunov theorems for Banach spaces ⋮ On spectral characterization of nonuniform hyperbolicity ⋮ The Spectrum of Vector Bundle Flows with Invariant Subbundles ⋮ Manifolds on the verge of a hyperbolicity breakdown ⋮ Evolution semigroups, translation algebras, and exponential dichotomy of cocycles ⋮ New conditions for (non)uniform behaviour of linear cocycles over flows ⋮ Quasi-hyperbolic semigroups ⋮ Hyperbolicity via evolution semigroups on \(L^p\) ⋮ Operator algebras and the Fredholm spectrum of advective equations of linear hydrodynamics ⋮ Immediate conditional hyperbolicity in dynamical systems

Cites Work

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• Centralizers of vector fields
• The spectrum of the adjoint representation and the hyperbolicity of dynamical systems
• Analyticity of spectral subbundles
• A spectral theory for linear differential systems
• Topological stability of Anosov flows and their centralizers
• A Generalized Poincare Stability Criterion
• A Geometric Criterion for Hyperbolicity of Flows
• Persistent manifolds are normally hyperbolic
• Invariant manifolds

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