Shape of limit cycles that bifurcate from non-Hamiltonian centers

Nonlinear Analysis, Theory, Methods and Applications

Volumn 43, Issue 7, 2001, Pages 837-859

  Giacomini, Hector ^a   Llibre, Jaume ^b   Viano, Mireille ^a  

^a Lab Biochim et Biol de la Nutr   (France)

^b UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL COMPLEXITY; INTEGRAL EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; POLES AND ZEROS; THEOREM PROVING;

NON-HAMILTONIAN CENTERS; POINCARE-MELNIKOV INTEGRAL METHOD; ZERO-ORDER EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0035284026     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00237-0     Document Type: Article

References (7)

1. A.A. Andronov et al., Theory of bifurcations of dynamical systems on a plane, Israel program for scientific translations, Jerusalem 1971.
2. Blows T.R., Perko L.M. Bifurcation of limit cycles from centers and separatrix cycles of planar analytic systems. SIAM Rev. 36:1994;341-376.
3. Chicone C., Jacobs M. Bifurcation of limit cycles from quadratic isochrones. J. Differential Equations. 91:1991;268-326.
4. S.N. Chows, C. Li, D. Wang, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge Univ. Press, Cambridge, 1994.
5. Giacomini H., Llibre J., Viano M. On the nonexistence, existence and uniqueness of limit cycles. Nonlinearity. 9:1996;501-516.
6. Giacomini H., Llibre J., Viano M. On the shape of limit cycles that bifurcate from Hamiltonian centers. Nonlinear Anal. Theory Methods Appl. 41:1997;523-537.
7. M. Viano, J. Llibre, H. Giacomini, Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor, Nonlinear Anal. Theory Methods Appl. (1998), submitted for publication.