Almost-invariant sets and invariant manifolds — Connecting probabilistic and geometric descriptions of coherent structures in flows

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Frontiers of chaotic advection (2014, methodology): “To identify and visualize invariant and almost-invariant sets, eigenvectors of the transition matrix are used to color the state space, as described in Dellnitz and Junge (2002); Froyland and Padberg (2009); Froyland et al. (2010b).”
Variational Approach for Learning Markov Processes from Time Series Data (2017, background): “5a that there is no transport between the left half and the right half of the domain and both subdomains are invariant sets with measure 12 (Froyland and Padberg 2009; Froyland and Padberg-Gehle 2014).”
Sparse Identification of Nonlinear Dynamics with Control (SINDYc) (2016, methodology): “, 2003), including the Perron-Frobenius operator (Froyland and Padberg, 2009), cluster reduced-order models based on probabilistic transition between various system behaviors (Kaiser et al.”
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].”