, Volume 60, Issue 6, pp 1765-1781

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

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Abstract

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.

Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 156–177, 1991.