A scaling law: How an attractor's volume depends on noise level

DOI10.1016/0167-2789(85)90085-5zbMath0577.58024OpenAlexW2057165083MaRDI QIDQ1065440

Ellen D. Yorke, Edward Ott, James A. Yorke

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0167-2789(85)90085-5

zbMATH Keywords

dimension of a strange attractor for systems with noise

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70)

Related Items (11)

Effects of randomness on chaos and order of coupled logistic maps ⋮ The influence of noise on the correlation dimension of chaotic attractors ⋮ Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds ⋮ The influence of measurement errors on the determination of the degrees of freedom of dynamic systems ⋮ A method of estimating the noise level in a chaotic time series ⋮ Effects of noise on some dynamical models in ecology ⋮ The influence of noise on a classical chaotic scatterer ⋮ On a classification of dynamic systems subject to noise ⋮ On linearisable noisy systems ⋮ On the influence of noise on the largest Lyapunov exponent and on the geometric structure of attractors ⋮ Confidence tori in the analysis of stochastic 3D-cycles

Cites Work

• The infinite number of generalized dimensions of fractals and strange attractors
• The Lyapunov dimension of strange attractors
• Hydrodynamic instabilities and the transition to turbulence
• Lyapunov theory and perturbation of stable and asymptotically stable systems
• Functional differential equations and approximation of fixed points. Proceedings, Bonn, July 1978
• Fat baker's transformations
• Strange attractors and chaotic motions of dynamical systems

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