Dynamics of generic 2-dimensional linear differential systems

DOI10.1016/j.jde.2006.03.009zbMath1105.37014OpenAlexW2032644908MaRDI QIDQ852580

Mário Bessa

Publication date: 15 November 2006

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

Full work available at URL: https://doi.org/10.1016/j.jde.2006.03.009

zbMATH Keywords

Lyapunov exponentsergodic theorydominated splitting

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Generic properties, structural stability of dynamical systems (37C20) Partially hyperbolic systems and dominated splittings (37D30)

Related Items

On integral separation of bounded linear random differential equations ⋮ On the Lyapunov exponent of certain \(SL (2,\mathbb R)\)-valued cocycles. II ⋮ Genericity of trivial Lyapunov spectrum for \(L^p\)-cocycles derived from second order linear homogeneous differential equations ⋮ Lyapunov exponents for linear homogeneous differential equations ⋮ Fine properties of \(L^p\)-cocycles which allow abundance of simple and trivial spectrum ⋮ Abundance of elliptic dynamics on conservative three-flows ⋮ The Lyapunov exponents of generic skew-product compact semiflows ⋮ The Lyapunov exponents of generic zero divergence three-dimensional vector fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Lyapunov exponents of generic volume-preserving and symplectic maps
• Dichotomies in stability theory
• Genericity of exponential dichotomy for two-dimensional differential systems
• A remark on non-uniform property of linear cocycles
• Structure and continuity of measurable flows
• Ergodic Properties of Linear Dynamical Systems
• Positive Lyapunov exponents for a dense set of bounded measurable SL(2, ℝ)-cocycles
• Genericity of zero Lyapunov exponents
• A generic bounded linear cocycle has simple Lyapunov spectrum
• On the Lyapounov exponent of certain SL\((2,\mathbb{R})\)-valued cocycles