Artículos de revistas
Limit Cycles Bifurcating From A K-dimensional Isochronous Center Contained In ℝ N With K ≤ N
Registro en:
Mathematical Physics Analysis And Geometry. , v. 10, n. 3, p. 237 - 249, 2007.
13850172
10.1007/s11040-007-9030-7
2-s2.0-38349188876
Autor
Llibre J.
Teixeira M.A.
Torregrosa J.
Institución
Resumen
The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in n with n ≤ k, when we perturb it in a class of C2 differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral. © 2007 Springer Science+Business Media B.V. 10 3 237 249 Abramowitz, M., Stegun, I.A., Bessel Functions J and Y, 9.1 (1972) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th Printing, pp. 358-364. , Dover New York Buicǎ, A., Françoise, J.P., Llibre, J., Periodic solutions of nonlinear periodic differential systems with a small parameter (2007) Commun. Pure Appl. Anal., 6, pp. 103-111 Champneys, A.R., Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics (1998) Phys. D, 112, pp. 158-186 Fabry, C., Mawhin, J., Properties of solutions of some forced nonlinear oscillations at resonance (1999) Proc. of the Second Conference on Nonlinear Analysis, pp. 103-118. , Progress in Nonlinear Analysis Tianjin, China Li, C., Christopher, C., Li, C., Abelian integrals and applications to weak Hilbert's 16 th problem (2007) Limit Cycles of Differential Equations. Advanced Courses in Mathematics, pp. 91-162. , CRM Barcelona, Birkhaüser Basel Li, J., Limit cycles bifurcated from a reversible quadratic center (2005) Qual. Theory Dyn. Syst., 6, pp. 205-216 Malkin, I.G., Some problems of the theory of nonlinear oscillations (1956) Gosudarstv. Izdat. Tehn.-Teor. Lit., , Moscow Russian Ostrovski, L., On the existence of stationary solitons (1979) Phys. Lett. A, 74, pp. 177-170 Peletier, L.A., Troy, W.C., Spatial patterns described by the extended Fisher-Komolgorov equation: Kinks (1995) Differential Integral Equations, 8, pp. 1279-1304 Peletier, L.A., Troy, W.C., (2001) Spatial Patterns. Higher Order Models in Physics and Mechanics Progress in Nonlinear Differential Equations and Their Applications, 5. , Birkhaüser Boston Roseau, M., (1966) Vibrations Non Linéaires et Théorie de la Stabilité (French) Springer Tracts in Natural Philosophy, 8. , Springer Berlin Heidelberg New York Sanchez, L., Boundary value problems for some fourth order ordinary differential equations (1990) Appl. Anal., 38, pp. 161-177 Sanders, J.A., Verhulst, F., Averaging methods in nonlinear dynamical systems (1985) Appl. Math. Sci., 59, pp. 1-247 Verhulst, F., (1991) Nonlinear Differential Equations and Dynamical Systems, Universitext, , Springer Berlin Heidelberg New York