Statistically optimal almost-invariant sets

By Gary Froyland. 2005

148 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7de441741cc7224c2187d2512e9508eea984f734

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In Computational Theory and Mathematics

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In Statistics and Probability

Citations in the corpus

Chaos as an intermittently forced linear system (2016, methodology): “Following the approach proposed by [34], almost-invariant sets can then be estimated by computing the associated reversible transition matrix and level-set thresholding its right eigenvectors.”
Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control (2015, methodology): “There are methods that identify almost invariant sets and coherent structures [61, 62] using set oriented methods [63].”
Almost-invariant sets and invariant manifolds — Connecting probabilistic and geometric descriptions of coherent structures in flows (2009, methodology): “A simple calculation [17] reveals that (11) is unchanged if Rn,τ is substituted for Pn,τ .”
Robust Perron cluster analysis in conformation dynamics (2005, background): “[9,10], which tackle more general problems, but in a different context and lower fixed dimensions.”
An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems (2012, methodology): “Regularity of singular vectors of Lε A standard heuristic for obtaining partitions from functions is to threshold on level sets; such an approach has been used in many previous applications of transfer operator methods to determine almost-invariant and metastable sets for autonomous or timeindepende”
Coherent structures and isolated spectrum for Perron–Frobenius cocycles (2008, methodology): “Numerical methods have been developed [DJ99, F05 , F08] for the computation of exceptional eigenfunctions and almostinvariant sets; these have been applied successfully in molecular dynamics [SHD99], astrodynamics [D+05], and ocean circulation [F+07].”