{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T20:48:09Z","timestamp":1759092489623,"version":"3.37.3"},"reference-count":71,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,6,2]],"date-time":"2018-06-02T00:00:00Z","timestamp":1527897600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,6,2]],"date-time":"2018-06-02T00:00:00Z","timestamp":1527897600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-15-1-2093"],"award-info":[{"award-number":["N00014-15-1-2093"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2020,10]]},"DOI":"10.1007\/s00332-018-9470-1","type":"journal-article","created":{"date-parts":[[2018,6,2]],"date-time":"2018-06-02T09:20:59Z","timestamp":1527931259000},"page":"2375-2404","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Go With the Flow, on Jupiter and Snow. Coherence from Model-Free Video Data Without Trajectories"],"prefix":"10.1007","volume":"30","author":[{"given":"Abd AlRahman R.","family":"AlMomani","sequence":"first","affiliation":[]},{"given":"Erik","family":"Bollt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,6,2]]},"reference":[{"issue":"5","key":"9470_CR1","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1109\/TPAMI.2007.70738","volume":"30","author":"C Antoni","year":"2008","unstructured":"Antoni, C., Vasconcelos, B.: Modeling, clustering, and segmenting video with mixtures of dynamic textures. IEEE Trans. Pattern Anal. Mach. Intell. 30(5), 909\u2013926 (2008)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"9470_CR2","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0925-7721(00)00022-5","volume":"17","author":"S Arya","year":"2000","unstructured":"Arya, S., Mount, D.M.: Approximate range searching. Comput. Geom. 17, 135\u2013163 (2000)","journal-title":"Comput. Geom."},{"key":"9470_CR3","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1017\/jfm.2013.249","volume":"726","author":"S Bagheri","year":"2013","unstructured":"Bagheri, S.: Koopman-mode decomposition of the cylinder wake. J. Fluid Mech. 726, 596\u2013623 (2013)","journal-title":"J. Fluid Mech."},{"key":"9470_CR4","unstructured":"Banisch, R., Koltai, P.: Understanding the geometry of transport: diffusion maps for Lagrangian trajectory data unravel coherent sets (2016), preprint. \narXiv:1603.04709"},{"key":"9470_CR5","doi-asserted-by":"crossref","first-page":"44005","DOI":"10.1209\/0295-5075\/98\/44005","volume":"98","author":"J Mahoney","year":"2012","unstructured":"Mahoney, J., Bargteil, D., Kingsbury, M., Mitchell, K.A., Solomon, T.: Invariant barriers to reactive front propagation in fluid flows. EPL 98, 44005 (2012)","journal-title":"EPL"},{"key":"9470_CR6","doi-asserted-by":"crossref","unstructured":"Basnayake, R., Bollt, E.M.: A Multi-Time Step Method to Compute Optical Flow with Scientific Priors for Observations of a Fluidic System, BIRS Book Chapter, Springer Proceedings in Mathematics and Statistics, Vol. 70, April, pp. 59\u201379 (2014)","DOI":"10.1007\/978-1-4939-0419-8_4"},{"key":"9470_CR7","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611972641","volume-title":"Applied and Computational Measurable Dynamics","author":"EM Bollt","year":"2013","unstructured":"Bollt, E.M., Santitissadeekorn, N.: Applied and Computational Measurable Dynamics. Society for Industrial and Applied Mathematics, Book Publisher, Philadelphia (2013)"},{"key":"9470_CR8","doi-asserted-by":"crossref","unstructured":"Bollt, E.M., Santitissadeekorn, N.: Applied and Computational Measurable Dynamics. Book Publisher: Society for Industrial and Applied Mathematics, Ch 5 On Network and Community Methods (2013)","DOI":"10.1137\/1.9781611972641"},{"issue":"448","key":"9470_CR9","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1093\/mind\/112.448.601","volume":"112","author":"L Bovens","year":"2003","unstructured":"Bovens, L., Hartmann, S.: Solving the riddle of coherence. Mind 112(448), 601\u2013633 (2003)","journal-title":"Mind"},{"key":"9470_CR10","doi-asserted-by":"crossref","first-page":"063005","DOI":"10.1103\/PhysRevE.92.063005","volume":"92","author":"J Li","year":"2015","unstructured":"Li, J., Boyer, C., Solomon, T., Mitchell, K.A.: Frozen reaction fronts in steady ows: a burning-invariant-manifold perspective. PRE 92, 063005 (2015)","journal-title":"PRE"},{"key":"9470_CR11","first-page":"047510133","volume":"22","author":"M Budisic","year":"2012","unstructured":"Budisic, M., Mohr, R.M., Mezic, I.: Applied Koopmanism. Chaos: an interdisciplinary. J. Nonlinear Sci. 22, 047510133 (2012)","journal-title":"J. Nonlinear Sci."},{"issue":"4","key":"9470_CR12","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.cviu.2008.11.005","volume":"113","author":"A Bugeau","year":"2009","unstructured":"Bugeau, A., P\u00e9rez, P.: Detection and segmentation of moving objects in complex scenes. ELSEVIER, Comput. Vis. Image Underst. 113(4), 459\u2013476 (2009)","journal-title":"ELSEVIER, Comput. Vis. Image Underst."},{"key":"9470_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00026-005-0237-z","volume":"9","author":"F Chung","year":"2005","unstructured":"Chung, F.: Laplacians and the Cheeger inequality for directed graphs. Ann. Comb. 9, 1\u201319 (2005)","journal-title":"Ann. Comb."},{"key":"9470_CR14","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.acha.2006.04.006","volume":"21","author":"RR Coifman","year":"2006","unstructured":"Coifman, R.R., Lafon, S.: Diffusion maps. Appl. Comput. Harmon. Anal. 21, 5\u201330 (2006)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9470_CR15","unstructured":"Denner, A., Junge, O., Matthes, D.: Computing Coherent Sets using the Fokker-Planck Equation. Preprint"},{"key":"9470_CR16","doi-asserted-by":"crossref","unstructured":"Dhillon, I.S., Guan, Y., Kulis, B.: Kernel k-means: spectral clustering and normalized cuts. In: Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 551\u2013556 (2004)","DOI":"10.1145\/1014052.1014118"},{"key":"9470_CR17","unstructured":"Fabregat, A., Poje, A.C., Mezic, I.: Finite-time Partitions for Lagrangian Structure Identification in Gulf Stream Eddy Transport (2016). \narXiv:1606.07382"},{"issue":"4","key":"9470_CR18","first-page":"215","volume":"97","author":"M Falorni","year":"1987","unstructured":"Falorni, M.: The discovery of the Great Red SPOT of Jupiter. J. Br. Astron. Assoc. 97(4), 215\u2013219 (1987)","journal-title":"J. Br. Astron. Assoc."},{"key":"9470_CR19","unstructured":"Fernandez, M., Stabafeb, D.: 8 Days, 10 Feet and the Snow Is not Done Yet. The New York Times, Feb 12 (2007)"},{"key":"9470_CR20","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1093\/analys\/63.3.194","volume":"63","author":"B Fitelson","year":"2003","unstructured":"Fitelson, B.: A probabilistic theory of coherence. Analysis 63, 194\u2013199 (2003)","journal-title":"Analysis"},{"key":"9470_CR21","unstructured":"Fortney, J.J., Marley, M.S., Saumon, D., Lodders, K.: Synthetic Spectra and Colors of Young Giant Planet Atmospheres: Effects of Initial Conditions and Atmospheric Metallicity. \narXiv:0805.1066v1\n\n [astro-ph]"},{"key":"9470_CR22","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1016\/j.physd.2010.03.009","volume":"239","author":"G Froyland","year":"2010","unstructured":"Froyland, G., Lloyd, S., Santitissadeekorn, N.: Coherent sets for nonautonomous dynamical systems. Physica D 239, 1527\u20131541 (2010)","journal-title":"Physica D"},{"key":"9470_CR23","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1016\/j.physd.2009.03.002","volume":"238","author":"G Froyland","year":"2009","unstructured":"Froyland, G., Padberg, K.: Almost-invariant sets and invariant manifolds\u2014connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D 238, 1507\u20131523 (2009)","journal-title":"Physica D"},{"key":"9470_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physd.2013.01.013","volume":"250","author":"G Froyland","year":"2013","unstructured":"Froyland, G.: An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D 250, 1\u201319 (2013)","journal-title":"Physica D"},{"key":"9470_CR25","doi-asserted-by":"crossref","first-page":"3587","DOI":"10.1088\/0951-7715\/28\/10\/3587","volume":"28","author":"G Froyland","year":"2015","unstructured":"Froyland, G.: Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity 28, 3587\u20133622 (2015)","journal-title":"Nonlinearity"},{"key":"9470_CR26","doi-asserted-by":"crossref","first-page":"043116","DOI":"10.1063\/1.3502450","volume":"20","author":"G Froyland","year":"2010","unstructured":"Froyland, G., Santitissadeekorn, N., Monahan, A.: Transport in time-dependent dynamical systems: finite-time coherent sets. Chaos 20, 043116 (2010)","journal-title":"Chaos"},{"key":"9470_CR27","doi-asserted-by":"crossref","unstructured":"Froyland, G., Padberg-Gehle, K.: Almost-invariant and finite-time coherent sets: directionality, duration, and diffusion. In: Bahsoun, W., Bose, C., Froyland, G. (eds.) Ergodic Theory, Open Dynamics, and Coherent Structures. Proceedings in Mathematics and Statistics, Vol. 70, Springer, pp. 171\u2013216 (2014)","DOI":"10.1007\/978-1-4939-0419-8_9"},{"key":"9470_CR28","doi-asserted-by":"crossref","first-page":"087406","DOI":"10.1063\/1.4926372","volume":"25","author":"G Froyland","year":"2015","unstructured":"Froyland, G., Padberg-Gehle, K.: A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. Chaos 25, 087406 (2015)","journal-title":"Chaos"},{"key":"9470_CR29","first-page":"103","volume":"44","author":"D Giannakis","year":"2015","unstructured":"Giannakis, D., Slawinska, J., Zhao, Z.: Spatiotemporal feature extraction with data-driven Koopman operators. J. Mach. Learn. Res. Proceedings 44, 103\u2013115 (2015)","journal-title":"J. Mach. Learn. Res. Proceedings"},{"key":"9470_CR30","unstructured":"Giannakis, D.: Data-driven spectral decomposition and forecasting of ergodic dynamical systems. Appl. Comput. Harmon. Anal. (2015) in review"},{"key":"9470_CR31","doi-asserted-by":"crossref","first-page":"063107","DOI":"10.1103\/PhysRevE.93.063107","volume":"93","author":"A Hadjighasem","year":"2016","unstructured":"Hadjighasem, A., Karrasch, D., Teramoto, H., Haller, G.: Spectral clustering approach to Lagrangian vortex detection. Phys. Rev. E 93, 063107 (2016)","journal-title":"Phys. Rev. E"},{"key":"9470_CR32","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1137\/140983665","volume":"58","author":"A Hadjighasem","year":"2016","unstructured":"Hadjighasem, A., Haller, G.: Geodesic transport barriers in Jupiter\u2019s atmosphere: a video-based analysis. SIAM Rev. 58, 69\u201389 (2016)","journal-title":"SIAM Rev."},{"issue":"1","key":"9470_CR33","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1063\/1.166479","volume":"10","author":"G Haller","year":"2000","unstructured":"Haller, G.: Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos 10(1), 99\u2013108 (2000)","journal-title":"Chaos"},{"key":"9470_CR34","doi-asserted-by":"crossref","first-page":"1680","DOI":"10.1016\/j.physd.2012.06.012","volume":"241","author":"G Haller","year":"2012","unstructured":"Haller, G., Beron-Vera, F.J.: Geodesic theory of transport barriers in two-dimensional flows. Physica D 241, 1680\u20131702 (2012)","journal-title":"Physica D"},{"key":"9470_CR35","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1146\/annurev-fluid-010313-141322","volume":"47","author":"G Haller","year":"2015","unstructured":"Haller, G.: Lagrangian coherent structures. Annu. Rev. Fluid. Mech. 47, 137\u2013162 (2015)","journal-title":"Annu. Rev. Fluid. Mech."},{"key":"9470_CR36","unstructured":"Kannan, R., Vempala, S., Vetta, A.: On clusterings\u2014good, bad and spectral. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science (2000)"},{"issue":"7","key":"9470_CR37","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1109\/TPAMI.2002.1017616","volume":"24","author":"T Kanungo","year":"2002","unstructured":"Kanungo, T., Mount, D., Netanyahu, N., Piatko, C., Silverman, R., Wu, A.: The efficient K-means clustering algorithm: analysis and implementation. IEEE Trans. Pattern Anal. Mach. Intell. 24(7), 881\u2013892 (2002)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"9470_CR38","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1093\/analys\/54.3.129","volume":"54","author":"P Klein","year":"1994","unstructured":"Klein, P., Warfield, T.: What price coherence? Analysis 54, 129\u2013132 (1994)","journal-title":"Analysis"},{"key":"9470_CR39","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.physd.2012.08.017","volume":"242","author":"Y Lan","year":"2013","unstructured":"Lan, Y., Mezic, I.: Linearization in the large of nonlinear systems and Koopman operator spectrum. Physica D 242, 42\u201353 (2013)","journal-title":"Physica D"},{"key":"9470_CR40","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1090\/S0002-9947-1982-0664049-X","volume":"273","author":"A Lasota","year":"1982","unstructured":"Lasota, A., Yorke, J.A.: Exact dynamical systems and the Frobenius\u2013Perron operator. Trans. Amer. Math. Soc. 273, 375\u2013384 (1982)","journal-title":"Trans. Amer. Math. Soc."},{"key":"9470_CR41","unstructured":"Lawler, E.: 4.5. Combinatorial Implications of Max-Flow Min-Cut Theorem, 4.6. Linear Programming Interpretation of Max-Flow Min-Cut Theorem. Combinatorial Optimization: Networks and Matroids. Dover. pp. 117\u2013120 (2001). ISBN 0-486-41453-1"},{"issue":"1","key":"9470_CR42","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1002\/pamm.201110415","volume":"11","author":"A Luttman","year":"2012","unstructured":"Luttman, A., Bollt, E.M., Basnayake, R., Kramer, S.: A stream function approach to optical flow with applications to fluid transport dynamics. Proc. Appl. Math. Mech. 11(1), 855\u2013856 (2012)","journal-title":"Proc. Appl. Math. Mech."},{"key":"9470_CR43","doi-asserted-by":"crossref","first-page":"033134","DOI":"10.1063\/1.4821188","volume":"23","author":"A Luttman","year":"2013","unstructured":"Luttman, A., Bollt, E.M., Basnayake, R., Kramer, S., Tullaro, N.B.: A stream function framework for estimating fluid flow from digital imagery. CHAOS 23, 033134 (2013)","journal-title":"CHAOS"},{"key":"9470_CR44","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/0040-9383(82)90023-4","volume":"21","author":"JN Mather","year":"1982","unstructured":"Mather, J.N.: Existence of quasi periodic orbits for twist homeomorphisms of the annulus. Topology 21, 457 (1982)","journal-title":"Topology"},{"key":"9470_CR45","first-page":"7 1330026","volume":"23","author":"T Ma","year":"2013","unstructured":"Ma, T., Bollt, E.M.: Relatively coherent sets as a hierarchical partition method. Int. J. Bifurc. Chaos 23, 7 1330026 (2013)","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"5","key":"9470_CR46","doi-asserted-by":"crossref","first-page":"1550076","DOI":"10.1142\/S0218127415500765","volume":"25","author":"T Ma","year":"2015","unstructured":"Ma, T., Bollt, E.M.: Shape coherence and finite-time curvature evolution. Int. J. Bifurc. Chaos 25(5), 1550076 (2015)","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"3","key":"9470_CR47","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1137\/130940633","volume":"13","author":"T Ma","year":"2014","unstructured":"Ma, T., Bollt, E.M.: Differential geometry perspective of shape coherence and curvature evolution by finite-time nonhyperbolic splitting. SIAM J. Appl. Dyn. Syst. (SIADS) 13(3), 1106\u20131136 (2014)","journal-title":"SIAM J. Appl. Dyn. Syst. (SIADS)"},{"key":"9470_CR48","doi-asserted-by":"crossref","first-page":"023112","DOI":"10.1063\/1.4941256","volume":"26","author":"T Ma","year":"2016","unstructured":"Ma, T., Ouellette, N., Bollt, E.M.: Stretching and folding in finite time. Chaos 26, 023112 (2016)","journal-title":"Chaos"},{"key":"9470_CR49","unstructured":"Meila, M., Shi, J.: A random walks view of spectral segmentation. AISTATS (2001)"},{"key":"9470_CR50","unstructured":"Meila, M., Shi, J.: Learning segmentation by random walks. Neural Inf. Process. Syst. 13, (2001)"},{"key":"9470_CR51","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1103\/RevModPhys.64.795","volume":"64","author":"JD Meiss","year":"1992","unstructured":"Meiss, J.D.: Symplectic maps. Var. Princ. Transp. Rev. Mod. Phys. 64, 795\u2013848 (1992)","journal-title":"Var. Princ. Transp. Rev. Mod. Phys."},{"key":"9470_CR52","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1093\/analys\/55.4.306","volume":"55","author":"T Merricks","year":"1995","unstructured":"Merricks, T.: On behalf of the coherentist. Analysis 55, 306\u2013309 (1995)","journal-title":"Analysis"},{"key":"9470_CR53","doi-asserted-by":"crossref","first-page":"087404","DOI":"10.1063\/1.4922026","volume":"25","author":"KA Mitchell","year":"2015","unstructured":"Mitchell, K.A.: Finite-time barriers to front propagation in two-dimensional fluid flows. Chaos 25, 087404 (2015)","journal-title":"Chaos"},{"key":"9470_CR54","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3836\/tjm\/1270128184","volume":"17","author":"M Mori","year":"1994","unstructured":"Mori, M.: On the convergence of the spectrum of Perron\u2013Frobenius operators. Tokyo J. Math. 17, 1\u201319 (1994)","journal-title":"Tokyo J. Math."},{"key":"9470_CR55","doi-asserted-by":"crossref","unstructured":"Murty, N.M., Devi, S.: Pattern Recognition: An Algorithmic Approach. V. (2011). ISBN 0857294946","DOI":"10.1007\/978-0-85729-495-1"},{"key":"9470_CR56","unstructured":"Nadler, B., Lafon, S., Coifman, R.R., Kevrekidis, I.G.: Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators. In: Advances in Neural Information Processing Systems 18 (2005)"},{"key":"9470_CR57","first-page":"849","volume":"2","author":"AY Ng","year":"2002","unstructured":"Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. Adv. Neural Inf. Process. Syst. 2, 849\u2013856 (2002)","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"9470_CR58","doi-asserted-by":"crossref","unstructured":"Onu, K., Huhn, F., Haller, G.: LCS Tool: A Computational Platform for Lagrangian Coherent Structures. \narXiv:1406.3527v1\n\n (2014)","DOI":"10.1016\/j.jocs.2014.12.002"},{"key":"9470_CR59","unstructured":"Papadimitriou, C.H., Steiglitz, K.: 6.1 The Max-Flow, Min-Cut Theorem. Combinatorial Optimization: Algorithms and Complexity. Dover. pp. 120\u2013128 (1998). ISBN 0-486-40258-4"},{"key":"9470_CR60","doi-asserted-by":"crossref","unstructured":"Perona, P., Freeman, W.T.: A factorization approach to grouping. In: Proceedings of the 5th European Conference on Computer Vision I, 665\u2013670 (1998)","DOI":"10.1007\/BFb0055696"},{"key":"9470_CR61","unstructured":"Riissmann, H.: On the existence of invariant curves of twist mappings of an annulus. Pre-print. Mainz, Germany (1981)"},{"key":"9470_CR62","volume-title":"Methods of Modern Mathematical Physics IV: Analysis of Operators","author":"M Reed","year":"1978","unstructured":"Reed, M., Simon, B.: Methods of Modern Mathematical Physics IV: Analysis of Operators. Academic Press, New York (1978)"},{"key":"9470_CR63","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1017\/S0022112009992059","volume":"641","author":"CW Rowley","year":"2009","unstructured":"Rowley, C.W., Mezic, I., Bagheri, S., Schlatter, P., Henningson, D.S.: Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115\u2013127 (2009)","journal-title":"J. Fluid Mech."},{"key":"9470_CR64","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.physd.2007.04.008","volume":"231","author":"N Santitissadeekorn","year":"2007","unstructured":"Santitissadeekorn, N., Bollt, E.M.: Identifying stochastic basin hopping and mechanism by partitioning with graph modularity. Physica D 231, 95\u2013107 (2007)","journal-title":"Physica D"},{"key":"9470_CR65","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.physd.2005.10.007","volume":"212","author":"SC Shadden","year":"2005","unstructured":"Shadden, S.C., Lekien, F., Marsden, J.E.: Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212, 271\u2013304 (2005)","journal-title":"Physica D"},{"key":"9470_CR66","unstructured":"Shi, S.J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. (2000)"},{"key":"9470_CR67","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1093\/bjps\/54.4.613","volume":"54","author":"T Shogenji","year":"2003","unstructured":"Shogenji, T.: A condition for transitivity in probabilistic support. Br. J. Philos. Sci. 54, 613\u2013616 (2003)","journal-title":"Br. J. Philos. Sci."},{"key":"9470_CR68","doi-asserted-by":"crossref","unstructured":"Surana, A.: Koopman operator based nonlinear dynamic textures. In: American Control Conference (ACC), pp. 1333\u20131338 (2015)","DOI":"10.1109\/ACC.2015.7170918"},{"key":"9470_CR69","unstructured":"Talmon, R., Coifman, R.R.: Empirical intrinsic geometry for nonlinear modeling and time series filtering. PNAS (2013) 110-31125351712540"},{"key":"9470_CR70","first-page":"1120","volume":"53","author":"SM Ulam","year":"1947","unstructured":"Ulam, S.M., von Neumann, J.: On combination of stochastic and deterministic processes. Bull. Am. Math. Soc. 53, 1120 (1947)","journal-title":"Bull. Am. Math. Soc."},{"key":"9470_CR71","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1007\/s00332-015-9258-5","volume":"25","author":"MO Williams","year":"2015","unstructured":"Williams, M.O., Kevrekidis, I.G., Rowley, C.W.: A data-driven approximation of the Koopman operator: extending dynamic mode decomposition. J. Nonlinear Sci. 25, 1307\u20131346 (2015)","journal-title":"J. Nonlinear Sci."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-018-9470-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-018-9470-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-018-9470-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T14:20:02Z","timestamp":1603203602000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-018-9470-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,2]]},"references-count":71,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["9470"],"URL":"https:\/\/doi.org\/10.1007\/s00332-018-9470-1","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"type":"print","value":"0938-8974"},{"type":"electronic","value":"1432-1467"}],"subject":[],"published":{"date-parts":[[2018,6,2]]},"assertion":[{"value":"20 November 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}