Dynamics of commuting systems on two-dimensional manifolds

Annali di Matematica Pura ed Applicata

Volumn 173, Issue 1, 1997, Pages 213-232

  Sabatini, M ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042710621     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/BF01783469     Document Type: Article

References (19)

1. V. I. ARNOLD, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York (1989).
2. N. P. BHATIA - G. P. SZEGÖ, Stability Theory of Dynamical Systems, Springer-Verlag, New York (1970).
3. C. CHICONE - M. JACOBS, Bifurcation of critical periods for plane vector fields, Trans. A.M.S., 312, 2 (1989), pp. 433-486.
4. G. F. D. DUFF, Limit cycles and rotated vector fields, Ann. Math., 57 (1953), pp. 15-31.
5. V. GUILLEMIN - A. POLLACK, Differential Topology, Prentice-Hall, Englewood Cliffs, New Jersey (1974).
6. P. HARTMAN, Ordinary Differential Equations, Birkhauser, Boston (1982).
7. N. A. LUKASHEVICH, Isochronicity of center for certain systems of differential equations, Diff. Equations, 1 (1965), pp. 220-226.
8. L. MARKUS, Parallel dynamical systems, Topology, 8 (1969), pp. 47-57.
9. G. H. MEISTERS, Personal communication.
10. L. MAZZI - M. SABATINI, A characterization of centres via first integrals, Jour. Diff. Eq., 76 2 (1988), pp. 222-237.
11. F. MARCHETTI - P. NEGRINI - L. SALVADORI - M. SCALIA, Liapunov Direct Method in Approaching Bifurcation Problems, Ann. Mat. Pura Appl., (IV), CVIII (1976), pp. 211-226.
12. P. J. OLVER, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York (1986).
13. G. R. SELL, Topological Dynamics and Ordinary Differential Equations, Van Nostrand Reinhold, New York (1971).
14. M. SABATINI, A connection between isochronous Hamiltonian centres and the Jacobian conjecture, preprint, Trento (1994).
15. M. SABATINI, Quadratic isochronous centres commute, preprint, Trento (1995).
16. M. SABATINI, Characterizing isochronous centres by Lie brackets, preprint, Trento (1995).
17. G. SANSONE - R. CONTI, Equazioni differenziali nonlineari, Cremonese, Roma (1956).
18. M. VILLARINI, Regularity properties of the period function near a center of a planar vector field, Nonlinear Analysis, T.M.A., 19, 8 (1992), pp. 787-803.
19. A. WALLACE, Differential Topology, W. A. Benjamin, New York (1968).