RELATIVELY COHERENT SETS AS A HIERARCHICAL PARTITION METHOD

DOI10.1142/S0218127413300267zbMath1275.37007arXiv1206.5767OpenAlexW3101357266MaRDI QIDQ2864934

Erik M. Bollt, Tian Ma

Publication date: 27 November 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.5767

zbMATH Keywords

Frobenius-Perron operatorrelative measurescoherent pairsrelatively coherent pairssubdivision flow chart

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Ergodic theorems, spectral theory, Markov operators (37A30) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (10)

Generalized Lagrangian coherent structures ⋮ Stretching and folding in finite time ⋮ An extended transfer operator approach to identify separatrices in open flows ⋮ Identifying finite-time coherent sets from limited quantities of Lagrangian data ⋮ Quantifying the Role of Folding in Nonautonomous Flows: The Unsteady Double-Gyre ⋮ A critical comparison of Lagrangian methods for coherent structure detection ⋮ Go with the flow, on Jupiter and snow. Coherence from model-free video data without trajectories ⋮ On star-convex volumes in 2-D hydrodynamical flows and their relevance for coherent transport ⋮ Linear response for the dynamic Laplacian and finite-time coherent sets ⋮ Shape Coherence and Finite-Time Curvature Evolution

Cites Work

• Almost-invariant sets and invariant manifolds - connecting probabilistic and geometric descriptions of coherent structures in flows
• An adaptive method for the approximation of the generalized cell mapping
• Finite approximations of Markov operators
• Control of an adaptive refinement technique of generalized cell mapping by system dynamics
• Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
• Symplectic maps, variational principles, and transport
• Transport in time-dependent dynamical systems: Finite-time coherent sets
• An adaptive subdivision technique for the approximation of attractors and invariant measures

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