Geodesic
Complicated Bifurcations of Periodic Solutions in Some System of Ode
Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 360-366

Voir la notice de l'article provenant de la source Cambridge University Press

In a vicinity of a stationary solution we consider a real analytic system of ODE of order four, depending on a small parameter. We look for families of periodic solutions which contract to the stationary solution, when the parameter tends to zero. We apply the general methods developed in [2] for the study of complex bifurcations and in [4] for local resolutions of singularities.
DOI : 10.4153/CMB-1996-043-0
Mots-clés : 34C20, 34C25 
Soleev, A. Complicated Bifurcations of Periodic Solutions in Some System of Ode. Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 360-366. doi: 10.4153/CMB-1996-043-0
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[1] 1. Bierstone, E. and Milman, P. D., Uniformization of analytic spaces, J. Amer. Math. Soc. 2( 1989), 801–836. Google Scholar

[2] 2. Bruno, A. D., Local Methods in Nonlinear Differential Equations, Springer-Verlag, Berlin, 1989. Google Scholar

[3] 3. Bruno, A. D., Bifurcation of the periodic solutions in the symmetric case of a multiple pair of imaginary eigenvalues, Selecta Math. Soviet. 12(1993), 1—12. Google Scholar

[4] 4. Bruno, A. D. and Soleev, A., Local uniformization of branches of a space curve and Newton polyhedra, St. Petersburg Math. J. 3( 1992), 53–841. Google Scholar

[5] 5. Bruno, A. D. and Soleev, A., First approximations of algebraic equations, Dokl. Akad. Nauk 335( 1994) 211—21%, (Russian), Russian Ac. Sci. Dokl. Math. 48(1994), 291–293, (English). Google Scholar

[6] 6. Drazin, P. G., Nonlinear Systems, Cambridge Univ. Press, 1992. Google Scholar

[7] 7. Holmes, P. J., Center manifolds, normal forms, and bifurcation of vector fields, Physica 2D( 1981 ), 449–481. Google Scholar

[8] 8. Khovanskii, A. G., Newton polyhedra (resolution of singularities), J. Soviet Math. 27(1984), 207–239. Google Scholar

[9] 9. Soleev, A., Algebraic aspects of the arrangement of periodic solutions of a Hamiltonian system, Qualitative and Analytic Methods in Dynamical Systems, Samarkand University, 1987, 55—67, (Russian). Google Scholar

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