The dimension formula for the Lorenz attractor

DOI10.1016/J.PHYSLETA.2011.01.034zbMath1242.34103OpenAlexW2139425917MaRDI QIDQ432880

Konstantin E. Starkov, Alexander Yu. Pogromsky, Gennady Alekseevich Leonov

Publication date: 4 July 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2011.01.034

zbMATH Keywords

Lorenz systemLyapunov dimension

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Attractors of solutions to ordinary differential equations (34D45)

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On differences and similarities in the analysis of Lorenz, Chen, and Lu systems ⋮ Exact Lyapunov dimension of attractors and convergence for the Lorenz system ⋮ Lyapunov functions in the attractor dimension theory ⋮ Formulas for the Lyapunov dimension of attractors of the generalized Lorenz system ⋮ Lyapunov Dimension Formulas for Lorenz-Like Systems ⋮ Constructing a New 3D Chaotic System with Any Number of Equilibria ⋮ Observation of nonlinear systems via finite capacity channels. II: Restoration entropy and its estimates ⋮ THE NONEQUIVALENCE AND DIMENSION FORMULA FOR ATTRACTORS OF LORENZ-TYPE SYSTEMS ⋮ The Lyapunov dimension and its estimation via the Leonov method ⋮ Lyapunov functions in the global analysis of chaotic systems ⋮ Maximal transport in the Lorenz equations ⋮ Linearization of the Lorenz system ⋮ Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor ⋮ On the Ultimate Dynamics of the Four-Dimensional Rössler System ⋮ Lyapunov functions in estimates of attractor dimensions for generalized Rössler systems

Cites Work

• Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds
• Maximum local Lyapunov dimension bounds the box dimension of chaotic attractors
• Applied Analysis of the Navier-Stokes Equations
• On the shape and dimension of the Lorenz attractor
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