DOI: 10.4213/sm9747e ISSN:
Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles
Andrei Valerevich Dukov- Algebra and Number Theory
The problem of the multiplicity of limit cycles appearing after a perturbation of a hyperbolic polycycle with generic set of characteristic numbers is considered. In particular, it is proved that the multiplicity of any limit cycle appearing after a perturbation in a smooth finite-parameter family does not exceed the number of separatrix connections forming the polycycle. Bibliography: 10 titles.