Some bifurcation problems of stability

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 3, 1997, Pages 1461-1467

  Goltser, Ya M ^a  

^a ARIEL UNIVERSITY   (Israel)

Author keywords

Bifurcation; Critical case of stability; Invariant torus; Lyapunov's method; Normal forms; Stability

Indexed keywords

EID: 0000726774     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00044-8     Document Type: Article

References (14)

1. MARSDEN J.E. & McCRACEN M. The Hopf bifurcation and its applications. Springer-Verlag, New York, 1976.
2. ARNOLD V. I. Geometrical methods in the theory of differential equations. Springer-Verlag, Berlin, 1983.
3. BIBIKOV YU. N. Bifurcation of a stable invariant torus by equilibrium state. Math. Notices 48, 15-19 (1990) (in Russian).
4. LIAPOUNOFF A. M., Problème génèral de la stabilité du mouvement. Princeton Univ. Press, Princeton, NJ (1949).
5. VERETENNIKOV V. G., Stability and oscillations of nonlinear systems Nauka, Moskow (1988) (in Russian).
6. SALVADORI L., Sulla riceradi una funzione di Liaponoff per un sistenie interessante la mecanica dei sisteme olonomi, Ricerche Mat., 11, 82-94 (1962).
7. MOLCHANOV A. M., Stability for the case of neutral linear approximation, Dokl. Akad. Nauk. SSSR 141, 24-27 (1961) (in Russian).
8. GOLTSER Ya. M., Stability of neutral fixed points of autonomos mapping with internal resonances, Differentsial'nye uravneniya 15, 2130-2141 (1979): English transl., Differential Equations 15, 1522-1531 (1980).
9. GOLTSER Ya. M., Stability of neutral fixed points of autonomos mapping with internal resonances, Differentsial'nye uravneniya 15, 2130-2141 (1979): English transl., Differential Equations 15, 1522-1531 (1980).
10. KUNITSYN A. L. & MARKEEV A. P., Stability in resonant cases, in Itogy nauki i techniki, Obshaya mechanika, 4, pp. 58-139. VINITI, Moskow (1979) (in Russian).
11. GOLTSER Ya. M., Stability of mappings with a spectrum on a unit circle, J. Math. Anal. Appl. 196, 841-860 (1995).
12. HALE J., Oscillations in nonlinear systems. McGraw-Hill, NJ (1963).
13. KUHN H. W. & TUCKER A. W., Linear inequalies and related systems. Princeton Univ. Press, Princeton, NJ (1956).
14. GALE D., The theory of linear economic models. McGraw-Hill, NJ (1960).