The fractal property of the Lorenz attractor

DOI10.1016/j.physd.2003.10.006zbMath1041.37013OpenAlexW2128018231MaRDI QIDQ1433703

Divakar Viswanath

Publication date: 1 July 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2003.10.006

zbMATH Keywords

periodic orbitsHausdorff dimensionLorenz equationsfractal structureSymbolic dynamicsmultiple precision computations

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Symbolic dynamics (37B10) Dimension theory of smooth dynamical systems (37C45) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Numerical problems in dynamical systems (65P99)

Related Items (20)

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Uses Software

• mctoolbox
• RODES

Cites Work

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• The structure of Lorenz attractors
• A rigorous ODE solver and Smale's 14th problem
• The Lindstedt--Poincaré Technique as an Algorithm for Computing Periodic Orbits
• Topological techniques for efficient rigorous computation in dynamics
• Recycling of strange sets: I. Cycle expansions
• Characterization of the Lorentz attractor by unstable periodic orbits
• Symbolic dynamics and periodic orbits of the Lorenz attractor*
• Deterministic Nonperiodic Flow
• Chaos in the Lorenz equations: A computer assisted proof. III: Classical parameter values

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