J. H. Wilkinson, The Algebraic Eigenvalue Problem, 1965.

R. A. Fitzhugh, Impulses and Physiological States in Theoretical Models of Nerve Membrane, Biophysical Journal, vol.1, issue.6, pp.445-466, 1961.
DOI : 10.1016/S0006-3495(61)86902-6

J. Murray, Mathematical biology, 1993.

P. C. Fife, Mathematical aspects of reacting and diffusing systems, 1979.
DOI : 10.1007/978-3-642-93111-6

K. Y. Tang, W. R. Graham, and J. Peraire, Active flow control using a reduced order model and optimum control, Fluid Dynamics Conference, pp.96-1946, 1996.
DOI : 10.2514/6.1996-1946

J. L. Lumley, The structure of inhomogeneous turbulent flows, In Atmospheric turbulence and Radio wave propagation, pp.166-78, 1967.

L. Sirovich, Turbulence and the dynamics of coherent structures, Quarterly of Applied Mathematics, issue.3, pp.561-590, 1987.

D. D. Kosambi, Statistics in Function Space, J. Indian Math. Soc, vol.7, pp.76-88, 1943.
DOI : 10.1007/978-81-322-3676-4_15

M. Loève, Fonctions aleatoire de second ordre, C. R. Acad. Sci. Paris, vol.220, 1945.

K. Karhunen, Zur spektral theorie stockasticher prozesse, Ann. Acad. Sci. Fenicae Ser, vol.1, p.34, 1946.

V. S. Pougachev, General theory of correlations of random functions, Izv. Akad. Nauk. SSSR, Ser. Mat, vol.17, pp.1401-1403, 1953.

A. M. Obukhov, Statistical description of continuous fields, Tr. Geophys. Int. Akad. Nauk. SSSR, vol.24, pp.3-42, 1954.

A. Papoulis, Probability, Random variables, and stochastic process, 1965.

V. R. Algazi and D. J. Sakrison, On the optimality of the Karhunen-Lo??ve expansion (Corresp.), IEEE Transactions on Information Theory, vol.15, issue.2, pp.319-340, 1969.
DOI : 10.1109/TIT.1969.1054286

C. A. Andrews, J. M. Davies, and G. R. Schwartz, Adaptative data compression, Proc. IEEE, pp.267-77, 1967.

R. W. Preisendorfer, Principal Component Analysis in Meteorology and Oceanography, 1953.

D. H. Gay and W. H. Ray, Identification and control of linear distributed parameter systems through the use of experimentally determined singular functions, Proc. IFAC Symp. Control of Distributed Parameter Systems, pp.173-79, 1986.

D. H. Gay and W. H. Ray, APPLICATION OF SINGULAR VALUE METHODS FOR IDENTIFICATION AND MODEL BASED CONTROL OF DISTRIBUTED PARAMETER SYSTEMS, Proc. IFAC Workshop on Model-Based Process Control, pp.95-102, 1988.
DOI : 10.1016/B978-0-08-035735-5.50018-8

L. Sirovich, Chaotic dynamics of coherent structures, Physica D: Nonlinear Phenomena, vol.37, issue.1-3, pp.126-171, 1989.
DOI : 10.1016/0167-2789(89)90123-1

L. Sirovich, Empirical Eigenfunctions and Low Dimensional Systems, Cent. Fluid Mech. Rep, pp.90-202, 1990.
DOI : 10.1007/978-1-4612-3156-1_5

P. J. Holmes, Can dynamical systems approach turbulence?, J. L. Lumley, Lect. Notes Phys, vol.357, pp.195-249, 1990.
DOI : 10.1007/3-540-52535-1_46

N. Aubry, P. Holmes, J. L. Lumley, and E. Stone, The dynamics of coherent structures in the wall region of a turbulent boundary layer, Journal of Fluid Mechanics, vol.15, issue.-1, pp.115-173, 1988.
DOI : 10.1146/annurev.fl.13.010181.002325

N. Aubry, On the hiddenbeauty of POD, Theoretical and Computational Fluid Dynamics, p.91

G. Berkooz, P. Holmes, and L. Lumley, The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows, Annual Review of Fluid Mechanics, vol.25, issue.1, pp.539-75, 1993.
DOI : 10.1146/annurev.fl.25.010193.002543

J. Delville, La décomposition orthogonale aux valeurs propres et l'analyse de l'organisation tridimensionnelle des écoulements turbulents cisaillés libres, Thése de Doctorat, 1995.

L. Cordier, F. Granier, J. Delville, C. Tenaud, W. Z. Shen et al., Modélisation par un système dynamique d'ordre faible du comportement à grande échelle d'une couche de mélange plane turbulente, 1997.

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