Normal forms and integrability of ODE systems

Programming and Computer Software

Volumn 32, Issue 3, 2006, Pages 139-144

  Bruno, A D ^a   Edneral, V F ^b  

^a KELDYSH INSTITUTE OF APPLIED MATHEMATICS   (Russian Federation)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; MATRIX ALGEBRA; NUMERICAL METHODS; PARAMETER ESTIMATION; RESONANCE;

EULER-POISSON SYSTEM; ODE SYSTEM; ONE-PARAMETER FAMILIES;

INTEGRATION;

EID: 33744746565     PISSN: 03617688     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0361768806030042     Document Type: Article

References (17)

1. Bruno, A.D., The Normal Form of Differential Equations, Dokl. Akad. Nauk SSSR, 1964, vol. 157, no. 6, pp. 1276-1279
2. [Soviet Math. Doklady, 1964, vol. 5, pp. 1105-1108].
3. Bruno, A.D., Normal Forms, Math. Comput. Simulation, 1998, vol. 45, nos. 5-6, pp. 413-427.
4. Bruno, A.D., Stepennaya geometriya v algebraicheskikh i differentsial'nykh uravneniyakh (Power Geometry in Algebraic and Differential Equations), Moscow: Nauka, 1998 [Elsevier, 2000].
5. Edneral, V.F., A Symbolic Approximation of Periodic Solutions of the Hénon-Heiles System by the Normal Form Method, Math. Comput. Simulation, 1998, vol. 45, nos. 5-6, pp. 445-463.
6. Golubev, V.V., Lektsii po integrirovaniyu uravnenii dvizheniya tyazhelogo tverdogo tela okolo nepodvizhnoi tochki (Lectures on Integration of Equations of Motion of a Rigid Body Around a Fixed Point), Moscow: GITTL, 1953.
7. Starzhinskii, V.M., Prikladnye metody nelineinykh kolebanii (Applied Methods in Nonlinear Oscillation), Moscow: Nauka, 1977, ch. 9.
8. Edneral, V.F. and Khanin, R., Application of the Resonant Normal Form to High Order Nonlinear ODEs Using MATHEMATICA, Nucl. Instrum. Methods Phys. Res. A, 2003, vol. 502, nos. 2-3, pp. 643-645.
9. Bruno, A.D., Analytical Form of Differential Equations, Tr. Mask. Mat. Obshch., 1971, vol. 25, pp. 119-262 ;
10. Bruno, A.D., Tr. Mask. Mat. Obshch., 1972, vol. 26, pp. 199-239
11. [Trans. Moscow Math. Soc., 1971, vol. 25, pp. 131-288 ;
12. Trans. Moscow Math. Soc., 1972, vol. 26, pp. 199-239].
13. Bruno, A.D., Lokal'nyi metod nelineinogo analiza differentsial'nykh uravnenii (Local Methods in Nonlinear Differential Equations), Moscow: Nauka, 1979 [Berlin: Springer, 1989].
14. Ziglin, S.L., Branching Solutions and Nonexistence of Integrals in the Hamiltonian Mechanics: I and II, Funkts. Anal. Ego Prilozh., 1982, vol. 16, no. 3, pp. 30-41;
15. Ziglin, S.L., Funkts. Anal. Ego Prilozh., 1983, vol. 17, no. 1, pp. 8-23
16. [Functional Analysis and Applications, 1982, vol. 16, no. 3;
17. Functional Analysis and Applications, 1983, vol. 17, no. 1].