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Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems.
Hamiltonian systems and transformation in Hilbert space
B. O. Koopman · 1931
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Deterministic nonperiodic flow
Edward N. Lorenz · 1963
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An equation for continuous chaos
O. E. Rössler · 1976
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Detecting strange attractors in turbulence
Floris Takens · 1981
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Embedology
Tim Sauer, James A. Yorke, and Martin Casdagli · 1991
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Time Series Prediction: Forecasting The Future And Understanding The Past
Andreas S. Weigend and Neil A. Gershenfeld, editors · 1993
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Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics
Andrzej Lasota and Michael C. Mackey · 1994
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On continuity of the Moore–Penrose and Drazin inverses
V. Rakočević · 1997
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The MATLAB ODE suite
Lawrence F. Shampine and Mark W. Reichelt · 1997
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Learning nonlinear dynamical systems using an EM algorithm
Z. Ghahramani and S. T. Roweis · 1999
Earlier work this paper cites.
Spectral properties of dynamical systems, model reduction and decompositions
Igor Mezić · 2005
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Multivariate phase space reconstruction by nearest neighbor embedding with different time delays
Sara P. Garcia and Jonas S. Almeida · 2005
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Reconstructing state spaces from multivariate data using variable delays
Yoshito Hirata, Hideyuki Suzuki, and Kazuyuki Aihara · 2006
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Kernel methods and the exponential family
Stéphane Canu and Alex Smola · 2006
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Spectral analysis of nonlinear flows
Clarence W. Rowley, Igor Mezić, Shervin Bagheri, Philipp Schlatter, and Dan S. Henningson · 2009
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Dynamic mode decomposition of numerical and experimental data
Peter J. Schmid · 2010
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Nonuniform state-space reconstruction and coupling detection
Ioannis Vlachos and Dimitris Kugiumtzis · 2010
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LIBSVM: A library for support vector machines
Chih-Chung Chang and Chih-Jen Lin · 2011
Cited alongside, same era.
Applied Koopmanism
Marko Budišić, Ryan Mohr, and Igor Mezić · 2012
Cited alongside, same era.
Variants of dynamic mode decomposition: Boundary condition, Koopman, and Fourier analyses
Kevin K. Chen, Jonathan H. Tu, and Clarence W. Rowley · 2012
Cited alongside, same era.
Differential Equations, Dynamical Systems, and an Introduction to Chaos
Morris W. Hirsch, Stephen Smale, and Robert L. Devaney · 2013
Cited alongside, same era.
Analysis of fluid flows via spectral properties of the Koopman operator
Igor Mezić · 2013
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Change-point detection in time-series data by relative density-ratio estimation
Song Liu, Makoto Yamada, Nigel Collier, and Masashi Sugiyama · 2013
Cited alongside, same era.
A Prony approximation of Koopman mode decomposition
Yoshihiko Susuki and Igor Mezić · 2015
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Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
Alexandre Mauroy and Jorge Goncalves · 2016
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Dynamic mode decomposition with reproducing kernels for Koopman spectral analysis
Yoshinobu Kawahara · 2016
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Linear dynamical neural population models through nonlinear embeddings
Yuanjun Gao, Evan W. Archer, Liam Paninski, and John P. Cunningham · 2016
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Composing graphical models with neural networks for structured representations and fast inference
Matthew Johnson, David K. Duvenaud, Alex Wiltschko, Ryan P. Adams, and Sandeep R. Datta · 2016
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Subspace dynamic mode decomposition for stochastic Koopman analysis
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A computational method to extract macroscopic variables and their dynamics in multiscale systems
Gary Froyland, Georg A. Gottwald, and Andy Hammerlindl · 2014
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On dynamic mode decomposition: Theory and applications
Jonathan H. Tu, Clarence W. Rowley, Dirk M. Luchtenburg, Steven L. Brunton, and J. Nathan Kutz · 2014
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Online and stochastic gradient methods for non-decomposable loss functions
Purushottam Kar, Harikrishna Narasimhan, and Prateek Jain · 2014
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Stochastic gradient VB and the variational auto-encoder
D. P. Kingma and M. Welling · 2014
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Discovering dynamic patterns from infectious disease data using dynamic mode decomposition
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Estimation of perturbations in robotic behavior using dynamic mode decomposition
Erik Berger, Mark Sastuba, David Vogt, Bernhard Jung, and Heni Ben Amor · 2015
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Naoya Takeishi, Yoshinobu Kawahara, and Takehisa Yairi · 2017
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Structured inference networks for nonlinear state space models
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Learning deep neural network representations for Koopman operators of nonlinear dynamical systems
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Ergodic theory, dynamic mode decomposition and computation of spectral properties of the Koopman operator
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Chaos as an intermittently forced linear system
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