The spectrum of the adjoint representation and the hyperbolicity of dynamical systems

DOI10.1016/0022-0396(80)90073-XzbMath0443.58019MaRDI QIDQ1144310

Carmen C. Chicone, Richard C. Swanson

Publication date: 1980

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

zbMATH Keywords

Anosov flowsflowLie derivativemeasure-preserving flowgeodesic flow on the unit tangent bundle of a Riemannian manifold of negative curvaturemeasure-preserving diffeomorphismsmooth diffeomorphismspectrum of the induced bounded linear operator on the continuous complex sections of the complexified tangent bundle

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Dynamical systems with hyperbolic behavior (37D99)

Related Items (7)

Cocycles and Mañe sequences with an application to ideal fluids ⋮ Spectral theory for linearizations of dynamical systems ⋮ Spectral Properties of Pullback Operators on Vector Bundles of a Dynamical System ⋮ The Spectrum of Vector Bundle Flows with Invariant Subbundles ⋮ Evolution semigroups, translation algebras, and exponential dichotomy of cocycles ⋮ Quasi-hyperbolic semigroups ⋮ Hyperbolicity via evolution semigroups on \(L^p\)

Cites Work

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• Tangent bundle connections and the geodesic flow
• A characterization of Anosov flows for geodesic flows
• Periodic flows on three-manifolds
• A Geometric Criterion for Hyperbolicity of Flows
• A Quasi-Anosov Diffeomorphism That is Not Anosov
• Quasi-Anosov Diffeomorphisms and Hyperbolic Manifolds
• Anosov does not Imply Infinitesimally Ergodic
• Persistent manifolds are normally hyperbolic
• A note on Anosov diffeomorphisms
• Isolated Invariant Sets for Flows on Vector Bundles

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