Principal part of multi-parameter displacement functions (CROSBI ID 209024)
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Podaci o odgovornosti
Mardešić, Pavao ; Saavedra, Mariana ; Uribe, Marco
engleski
Principal part of multi-parameter displacement functions
This paper deals with a perturbation problem from a period annulus, for an analytic Hamiltonian system [J.-P. Françoise, Ergodic Theory Dynam. Systems 16 (1996), no. 1, 87–96 ; L. Gavrilov, Ann. Fac. Sci. Toulouse Math. (6) 14(2005), no. 4, 663–682. The authors consider the planar polynomial multi-parameter deformations and determine the coefficients in the expansion of the displacement function generated on a transversal section to the period annulus. Their first result gives a generalization to the Françoise algorithm for a one-parameter family, following [J.-P. Françoise and M. Pelletier, J. Dyn. Control Syst. 12 (2006), no. 3, 357–369. The second result expresses the principal terms in the division of the displacement function in the Bautin ideal. The methods are illustrated with interesting examples, such as the versal unfolding of the Hamiltonian triangle center.
Hamiltonian system; perturbation; triangle center
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Podaci o izdanju
136 (7)
2012.
752-762
objavljeno
0007-4497
10.1016/j.bulsci.2012.02.006