Journal of Soviet Mathematics

, Volume 60, Issue 6, pp 1765–1781

The asymptotics of the return map of a singular point with fixed Newton diagram

  • F. S. Berezovskaya
  • N. B. Medvedeva

DOI: 10.1007/BF01102588

Cite this article as:
Berezovskaya, F.S. & Medvedeva, N.B. J Math Sci (1992) 60: 1765. doi:10.1007/BF01102588


We exhibit a large class of nondegenerate singular points in which necessary and sufficient conditions are given for monodromy. We compute the generalized first Lyapunov value, which is expressed in terms of the Newton diagram of the singular point. The computational algorithm proposed is based on writing the return map as the composition of transition mappings constructed using the diagram. The nonvanishing of the generalized first Lyapunov value is a sufficient condition for the existence of a focus. Bibliography: 8 titles.

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • F. S. Berezovskaya
  • N. B. Medvedeva

There are no affiliations available