On the Approximation of Koopman Spectra for Measure Preserving Transformations

DOI10.1137/18M1175094zbMath1436.28011arXiv1803.03920OpenAlexW2968477129WikidataQ127362854 ScholiaQ127362854MaRDI QIDQ5238236

Igor Mezić, Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran

Publication date: 28 October 2019

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.03920

zbMATH Keywords

measure preserving transformationKoopman operatorperiodic approximations

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Eigenvalue problems for linear operators (47A75) Linear operator approximation theory (47A58) Dynamical aspects of twist maps (37E40)

Related Items

Modern Koopman Theory for Dynamical Systems, Nonlinear observability via Koopman analysis: characterizing the role of symmetry, Towards global optimal control via Koopman lifts, Generative Stochastic Modeling of Strongly Nonlinear Flows with Non-Gaussian Statistics, The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems, Prandtl–Batchelor theorem for flows with quasiperiodic time dependence, Geometric considerations of a good dictionary for Koopman analysis of dynamical systems: cardinality, ``primary eigenfunction, and efficient representation, On the Approximation of Koopman Spectra of Measure-Preserving Flows, Detecting regime transitions in time series using dynamic mode decomposition

Uses Software

• GAIO

Cites Work

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• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• Exact numerical studies of Hamiltonian maps: Iterating without roundoff error
• Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture
• Comparison of systems with complex behavior
• Finite approximations of Frobenius-Perron operators. A solution of Ulam's conjecture to multi-dimensional transformations
• Passive scalars, three-dimensional volume-preserving maps, and chaos
• Data-driven spectral analysis of the Koopman operator
• Spectral properties of dynamical systems, model reduction and decompositions
• Entropy and approximation of measure preserving transformations
• In general a measure preserving transformation is mixing
• Measure-preserving homeomorphisms and metrical transitivity
• On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
• Applied Koopmanism
• Dynamic mode decomposition of numerical and experimental data
• Spectral analysis of nonlinear flows
• On the Approximation of Complicated Dynamical Behavior
• Constructing Permutations that Approximate Lebesgue Measure Preserving Dynamical Systems Under Spatial Discretization
• Hamiltonian Systems and Transformation in Hilbert Space
• A method for visualization of invariant sets of dynamical systems based on the ergodic partition
• Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets
• Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
• Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets
• APPROXIMATIONS IN ERGODIC THEORY
• Approximation of measure preserving transformations
• Approximation Theories for Measure Preserving Transformations