Transitivity and invariant measures for the geometric model of the Lorenz equations

DOI10.1017/S0143385700002674zbMath0558.28011MaRDI QIDQ3223085

Clark Robinson

Publication date: 1984

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

topologically transitiveergodic measurelocally eventually ontoone- dimensional Poincaré mapsperturbations of the geometric model of the Lorenz equations

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory (37A99)

Related Items (5)

Phase plane analysis using the Poincaré map ⋮ A degenerate singularity generating geometric Lorenz attractors ⋮ Existence of \(C^k\)-invariant foliations for Lorenz-type maps ⋮ Sinai-Ruelle-Bowen measures for contracting Lorenz maps and flows ⋮ Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps

Cites Work

• Hyperbolicity conditions for the Lorenz model
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Structural stability of Lorenz attractors
• The structure of Lorenz attractors
• The Lorenz equations: bifurcations, chaos, and strange attractors
• Generalized bounded variation and applications to piecewise monotonic transformations
• Hölder Continuous Derivatives and Ergodic Theory
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• Ergodic Transformations from an Interval Into Itself
• Some Metric Properties of Piecewise Monotonic Mappings of the Unit Interval

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