The computation of Lyapunov exponents via spatial integration with application to blowout bifurcations

DOI10.1016/S0045-7825(98)00196-0zbMath0945.65142WikidataQ126805879 ScholiaQ126805879MaRDI QIDQ1965143

Michael Dellnitz, Philip J. Aston

Publication date: 5 October 2000

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

dynamical systeminvariant measureLyapunov exponentblowout bifurcationDuffing oscillatorsHenon mapspatial integration

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Numerical bifurcation problems (65P30) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (3)

A hybrid method for computing Lyapunov exponents ⋮ Error analysis of a hybrid method for computing Lyapunov exponents ⋮ Computing the invariant measure and the Lyapunov exponent for one-dimensional maps using a measure-preserving polynomial basis

Cites Work

• Unnamed Item
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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• General random perturbations of hyperbolic and expanding transformations
• Computation of the largest Lyapunov exponent by the generalized cell mapping
• Analycity properties of the characteristic exponents of random matrix products
• A subdivision algorithm for the computation of unstable manifolds and global attractors
• Computations in dynamical systems via random perturbations
• An adaptive method for the approximation of the generalized cell mapping
• GLOBAL ANALYSIS BY CELL MAPPING
• SYMMETRY BREAKING BIFURCATIONS OF CHAOTIC ATTRACTORS
• From attractor to chaotic saddle: a tale of transverse instability
• Ergodic theory of chaos and strange attractors

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