A note on Kaplan-Yorke-type estimates on the fractal dimension of chaotic attractors

DOI10.1016/0960-0779(93)90007-NzbMath0783.58044OpenAlexW2026152656MaRDI QIDQ1313121

Zhi Min Chen

Publication date: 20 March 1994

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0960-0779(93)90007-n

zbMATH Keywords

chaotic attractorfractal dimensionestimateKaplan-Yorke-type numbers

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fractals (28A80)

Related Items

The \(\varepsilon\)-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors, Hausdorff and fractal dimension estimates for invariant sets of non-injective maps, The Hausdorff measure of chaotic sets of adjoint shift maps, Qualitative feature extractions of chaotic systems, A note on the fractal dimension of attractors of dissipative dynamical systems, Can a polynomial interpolation improve on the Kaplan-Yorke dimension?, On the relation between Rayleigh-Bénard convection and Lorenz system

Cites Work

• Chaotic attractors of an infinite-dimensional dynamical system
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The Lyapunov dimension of strange attractors
• A two-dimensional mapping with a strange attractor
• Dimensions and entropies of strange attractors from a fluctuating dynamics approach
• The local structure of a chaotic attractor in four dimensions
• Measuring the strangeness of strange attractors
• Infinite-dimensional dynamical systems in mechanics and physics
• Multi-dimensional Cantor sets in classical and quantum mechanics
• Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors
• On turbulence and complex dynamic in a four-dimensional Peano-Hilbert space
• Statistical mechanics of multi-dimensional Cantor sets, Gödel theorem and quantum spacetime
• Internal Cantor distance and entropy of multidimensional Peano-Hilbert spaces
• Local and global Lyapunov exponents
• Global lyapunov exponents, kaplan-yorke formulas and the dimension of the attractors for 2D navier-stokes equations
• Determining modes and fractal dimension of turbulent flows
• Some applications of Hausdorff dimension inequalities for ordinary differential equations
• Deterministic Nonperiodic Flow
• Local Lyapunov exponents and a local estimate of Hausdorff dimension
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item