Vers une notion de dérivation fonctionnelle causale

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1. [1] J.F. Barrett, The use of functionals in the analysis of non-linear physical systems, J. Electronics Control, t. 15, 1963, p. 567-615. 
2. [2] J. Berstel et C. Reutenauer, Les séries rationnelles et leurs langages, Masson, Paris, 1984. Zbl0573.68037MR745968
3. [3] N. Bourbaki, Algèbre I (chap. 1 à 3), Hermann, Paris, 1970. Zbl0211.02401MR274237
4. [4] K.-T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. of Math., t. 65, 1957, p. 163-178. Zbl0077.25301MR85251
5. [5] K.-T. Chen, Algebraic paths, J. Algebra, t. 10, 1968, p. 8-36. Zbl0204.33803MR229630
6. [6] K.-T. Chen, Iterated path integrals, Bull. Amer. Math. Soc., t. 83, 1977, p. 831-879. Zbl0389.58001MR454968
7. [7] W.N. Findley, J.-S. Lai et K. Onaran, Creep and Relaxation of Nonlinear Visco-elastic Materials, North-Holland, Amsterdam, 1976. Zbl0345.73034MR431847
8. [8] M. Fliess, Fonctionnelles causales non linéaires et indéterminées non commutatives, Bull. Soc. Math. France, t. 109, 1981, p. 3-40. Zbl0476.93021MR613847
9. [9] M. Fliess, Réalisation locale des systèmes non linéaires, algèbres de Lie filtrées transitives et series génératrices non commutatives, Inventiones Math., t. 71, 1983, p. 521-537. Zbl0513.93014MR695904
10. [10] M. Fliess, On the concept of derivatives and Taylor expansions for nonlinear input-output systems, Proc. 22nd IEEE Conf. Decision Control, p. 643-646, San Antonio, TX, 1983. 
11. [11] M. Fliess, M. Lamnabhi et F. Lamnabhi-Lagarrigue, An algebraic approach to nonlinear functional expansions, IEEE Trans. Circuits Systems, t. 30, 1983, p. 554-570. Zbl0529.34002MR715510
12. [12] M. Fliess et F. Lamnabhi-Lagarrigue, Application of a new functional expansion to the cubic anharmonic oscillator, J. Math. Physics, t. 23, 1982, p. 495-502. MR649526
13. [13] M. Fliess et D. Normand-Cyrot, Algèbres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et intégrales itérées de K. T. Chen, Séminaire de ProbabilitésXVI1980/1981, J. Azéma et M. Yor eds., p. 257-267, Lect. Notes Math.920, Springer-Verlag, Berlin, 1982. Zbl0495.60064MR658689
14. [14] F. Hausdorff, Die symbolische Exponentialformel in derGruppentheorie, Leipziger Ber., t. 58, 1906, p. 19-48. Zbl37.0176.02JFM37.0176.02
15. [15] W. Magnus, A. Karrass et D. Solitar, Combinatorial Group Theory, Interscience, New York, 1966. 
16. [16] U. Oberst, Actions of formal groups on formal schemes. Application to control theory and combinatorics, Séminaire M.-P. Malliavin, Paris, 1983. Zbl0617.14029
17. [17] R. Ree, Lie elements and an algebra associated with shuffles, Ann. of Math., t. 68, 1958, p. 210-220. Zbl0083.25401MR100011
18. [18] J. Riordan, An Introduction to CombinatorialAnalysis, Wiley, New York, 1958. Zbl0078.00805MR96594
19. [19] G. Rosen, Formulations of Classical and Quantum Dynamical Theory, Academic Press, New York, 1969. Zbl0195.28102MR273906
20. [20] G.-C. Rota, B. Sagan et P.R. Stein, A cyclic derivative in noncommutative algebra, J. Algebra, t. 64, 1980, p. 54-75. Zbl0428.16036MR575782
21. [21] W.J. Rugh, Nonlinear System Theory, TheJohns Hopkins University Press, Baltimore, 1981. Zbl0666.93065MR713994
22. [22] J. Rzewuski, Field Theory, t. 2, Polish Scientific Publishers, Varsovie, et, Iliffe Books, Londres, 1969. 
23. [23] M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, Wiley, New York, 1980. Zbl0501.93002MR562917
24. [24] R. Siegmund-Schultze, Die Anfänge der Funktionalanalysis und ihr Platz im Umwälzungsprozess der Mathematik um1900, Arch. History Exact Sc., t. 26, 1982, p. 13-71. Zbl0514.46001MR664469
25. [25] M.E. Sweedler, Hopf Algebras, Benjamin, New York, 1968. Zbl0194.32901MR252485
26. [26] V. Volterra, Leçons sur les fonctions de lignes, Gauthier-Villars, Paris, 1913. 
27. [27] V. Volterra et J. Pérès, Théorie générale des fonctionnelles, t. 1, Gauthier-Villars, Paris. 1936. Zbl0015.30501JFM62.0455.01