Nilpotent normal form via Carleman linearization (for systems of ordinary differential equations)

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Nilpotent normal form via Carleman linearization (for systems of ordinary differential equations)

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1991 international symposium on Symbolic and algebraic computation table of contents

Bonn, West Germany

Pages: 281 - 288

Year of Publication: 1991

ISBN:0-89791-437-6

Authors

Guoting Chen	Département de Mathématique, Université Louis Pasteur, 7, Rue René Descartes, 67084 Strasbourg France
Jean Della Dora	LMC-INPG, 46 Av. Félix-Viallet, 38031 Grenoble France
Laurent Stolovitch	LMC-INPG, 46 Av. Félix-Viallet, 38031 Grenoble France

Sponsors

GMD : German Natl Research Ctr for Information Tech. - Gesellschft
German Comp Soc : GI - Gesellshaft for Informatik
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 18, Citation Count: 3

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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.

	1	D. V. Anosov , S. Kh. Aranson , V. I. Arnold , I. U. Bronshtein , Yu. S. Il'yashenko , V. Z. Grines, Ordinary differential equations and smooth dynamical systems, Springer-Verlag New York, Inc., New York, NY, 1997
	2	R. Bellman and J. M. Richardson, On some questions arising in the approximate solution of nonlinear differential equations, Quart. Appl. Math. 20(1963), 333-339.
	3	V. N. Bogaevski and A. Yd. Povzner, A nonlinear generalization of the shearing transformation. Funvt. Anal. and Appl. 16(1982),45- 46.
	4	A. D. Bruno, Local method of nonlinear analysis of differential equations, Springer-Verlag, 1979.
	5	T. Carleman, Application de la thdorie des dquations intdgrates lindaires aux syst~mes d'dquations diffdrentielles nonlindaires, Acta Math. 59(1932), 63-68.
	6	G. Chen, Computing the normal forms of matrices depending on parameters, Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation, p.242-249, July 17-19, 1989, Portland, Oregon, United States [doi>10.1145/74540.74570]
	7	G. Chen and J. Della Dora, Nilpotent normal form of systems of nonlinear differential equations: algorithm and examples, Preprint, 1990.
	8	R. Cushman and J. Sanders, Nilpotent normal forms and representation theory of sis(R), in: Multiparameter bifurcation theory, eds. M. Golubitsky and J. Guckenheimer, Contemporary Mathematics, vol. 56, Amer Math. Soc. Providence, 1986, 31-35.
	9	R. Cushman and J. A. Sanders, A survey of invariant theory applied to normal form of vector fields with nilpotent linear part, Proceeding of Invariant Theory, Springer New York 1990, 82-106.
	10	J. Della Dora and L. Stolovitch, Poincard-Dulac normal form, Preprint.
	11	H. Poincar@, Notes sur les propridtds des fonctions ddfinies par des dquations diffdrentielles, Journal de l'Ecole Polytechnique, 45~ cahier, 1878, 13-26.
	12	W. H. Steeb and F. Wilhelm, Nonlinear autonomous system of differential equations and Carleman linearization procedure, J. Math. Anal. and Appl. 77 (1980), 601-611.
	13	F. Takens, Singularities of vector fields, Publications Math~matiques I.H.E.S. 43(1974), 47-100.
	14	A. Trampus, A canonical basis for the matrix transformation X ---. AX +XB, 3. of Math. Anal. and Appl. 14(1966), 242-252.
	15	C.A. Tsiligiannis and G. Lyberatos, Normal forms, resonance and bifurcation analysis via the Carleman linearization, j. Math. Anal. and Appl. 139 (1989), 123-138.
	16	C. A. Tsiligiannis and G. Lyberatos, Steady state bifurcation and exact multiplicity condition via Carleman linearization, J. Math. Anal. and Appl. 126(1987), 143-160.

CITED BY 3

	Guoting Chen , Jean Della Dora, Rational normal form for dynamical systems by Carleman linearization, Proceedings of the 1999 international symposium on Symbolic and algebraic computation, p.165-172, July 28-31, 1999, Vancouver, British Columbia, Canada
	P. E. Crouch , R. L. Grossman, The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomial coefficients using trees, Papers from the international symposium on Symbolic and algebraic computation, p.89-94, July 27-29, 1992, Berkeley, California, United States
	L. Vallier, An algorithm for the computation of normal forms and invariant manifolds, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, p.225-233, July 06-08, 1993, Kiev, Ukraine