ISSN 1002-1027  CN 11-2952/G2

Acta scientiarum naturalium Universitatis Pekinensis

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The Bifurcation Phenomena of Polycycle S(3) of Hamiltonian System Under Small Perturbations

LI Baoyi1, ZHANG Zhifen2   

  1. 1Department of Mathematics, Tianjin Normal University, Tianjin, 300073; 2School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:1997-06-19 Online:1998-09-20 Published:1998-09-20

Abstract: By means of finitely-smooth normal form theory and the method of infinitesimal analysis, it is proved that the cyclicity of polycycle S(3) of planar Hamiltonian system under small perturbations with certain nondegenerate condition is 3, thus the results of A.Mourtada about the cyclicity of isolated S(3) is generalized.