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Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge.
Hamiltonian systems and transformation in hilbert space
B.O. Koopman · 1931
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Floris Takens · 1981
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Andrzej Lasota and Michael C. Mackey · 1994
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Igor Mezić · 2005
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Clarence W. Rowley, Igor Mezic, Shervin Bagheri, Philipp Schlatter, and Dan S. Henningson · 2009
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Relationship between singular spectrum analysis and fourier analysis: Theory and application to the monitoring of volcanic activity
Enrico Bozzo, Roberto Carniel, and Dario Fasino · 2010
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Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2010
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Applied Koopmanism a)
Marko Budišić, Ryan Mohr, and Igor Mezić · 2012
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Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability
Dimitrios Giannakis and Andrew J Majda · 2012
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Advanced mathematical methods for scientists and engineers I: Asymptotic methods and perturbation theory
Carl M Bender and Steven A Orszag · 2013
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Perturbation methods in applied mathematics
Jirayr Kevorkian and Julian D Cole · 2013
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Linearization in the large of nonlinear systems and Koopman operator spectrum
Yueheng Lan and Igor Mezić · 2013
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Frank Noé and Feliks Nuske · 2013
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The optimal hard threshold for singular values is 4 / 3 4/\sqrt{3}
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Feliks Nüske, Bettina G Keller, Guillermo Pérez-Hernández, Antonia SJS Mey, and Frank Noé · 2014
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On dynamic mode decomposition: theory and applications
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz · 2014
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Yoshihiko Susuki and Igor Mezić · 2015
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Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator
Qianxiao Li, Felix Dietrich, Erik M. Bollt, and Ioannis G. Kevrekidis · 2017
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Bayesian dynamic mode decomposition
Naoya Takeishi, Yoshinobu Kawahara, Yasuo Tabei, and Takehisa Yairi · 2017
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Learning Koopman invariant subspaces for dynamic mode decomposition
Naoya Takeishi, Yoshinobu Kawahara, and Takehisa Yairi · 2017
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Subspace dynamic mode decomposition for stochastic Koopman analysis
Naoya Takeishi, Yoshinobu Kawahara, and Takehisa Yairi · 2017
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Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
Christoph Wehmeyer and Frank Noé · 2017
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Continuous analogues of matrix factorizations
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Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
Bingni W. Brunton, Lise A. Johnson, Jeffrey G. Ojemann, and J. Nathan Kutz · 2016
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Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
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