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Rational normal form for dynamical systems by Carleman linearization
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Source International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1999 international symposium on Symbolic and algebraic computation table of contents
Vancouver, British Columbia, Canada
Pages: 165 - 172  
Year of Publication: 1999
ISBN:1-58113-073-2
Authors
Guoting Chen  UFR de Mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq, France
Jean Della Dora  LMC-IMAG, 51 Rue des Mathématiques, B. P. 53, 38041 Grenoble Cedex 9, France
Sponsors
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics
Publisher
ACM  New York, NY, USA
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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
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ARNOLD, V. I. Geometrical methods in the theory of ordinary differential equations. Springer-Verlag, 1983.
 
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BRUNO, A. D. Local method of nonlinear analysis of differential equations. Springer-Verlag, 1979.
 
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CARLEMAN, T. Application de la th~orie des ~quations int~grales lin~aires aux syst~mes d'~quations diffrentielles nonlin~aires. Acta Math. 59 (1932), 63.68.
4
 
5
CHEN, G., AND DELLA DORA, J. An algorithm for computing a new normal form for dynamical systems. in preparation (1999).
 
6
CHEN, G., AND DELLA DORA. J. Further reductions of normal forms for dynamical systems, submitted (1999).
7
 
8
CHOW, S. N., AND HALE, J. K. Methods of bifurcation theory. Springer-Verlag, 1982.
 
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CHOW, S. N., LI, C., AND WANG, D. Normal forms and bifurcation of planar vector fields. Cambridge University Press, 1994.
 
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CHUA, L. O., AND KOKUBU, H. Normal forms for nonlinear vector fields- part ii: Applications. IEEE Trans. on Circuits and Sys. 36 (1989), 51.70.
 
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CUSHMAN, R., AND SANDERS, J. Nilpotent normal forms and representation theory of sl2(r). In Multiparameter bifurcation theory, M. Golubitsky and J. Guckenheimer, Eds., vol. 56 of Contemporary Mathematics. Amer Math. Soc., 1986, pp. 31-35.
 
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GAETA, G. Poincar~ renornlalized forms. Preprint, mp-arc 96-263 (1996), 1-23.
 
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GIL, I. Contribution ~ l'alg~bre lin~aire formelle: formes normales de matrices et applications. PhD thesis, Institut National Polytechnique de Grenoble, 1993.
 
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OZELLO, P. CaleuI exact des formes de Jordan et de Frobenius d'une matrice. PhD thesis, Universit~ de Grenoble 1, 1987.
 
16
POINCAR~, H. Notes sur les properi~t~s des fonctions d~finies par des ~quations diff~rentielles. Journal de l'Ecole Polytechnique 45 (1878), 13-26.
 
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STEEB, W. H., AND WILHELM, F. Nonlinear autonomous system of differential equations and carleman linearization procedure. J. Math. Anal. Appl. 77 (1980), 601-611.
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TAKENS, F. Normal forms for certain singularities of vectorfields. Ann. Inst. Fourier 23 (1973), 163-195.
 
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TAKENS, F. Singularities of vector fields. Publ. Math. I.H.E.S. 43 (1974), 47-100.
 
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TSILIGIANNIS, C. A., AND LYBERATOS, G. Normal forms, resonance and bifurcation analysis via the carleman linearization. J. Math. Anal. Appl. 139 (1989), 123-138.
 
22
USIIlKl, S. Normal forms for singularities of vector fields. Japan J. Appl. Math. 1 (1984), 1-34.

Collaborative Colleagues:
Guoting Chen: colleagues
Jean Della Dora: colleagues