Relations of Formal Diffeomorphisms and the Center Problem

  title={Relations of Formal Diffeomorphisms and the Center Problem},
  author={Isao Nakai and Kana Yanai},
  journal={Moscow Mathematical Journal},
A word of germs of holomorphic diffeomorphisms of (C, 0) is a composite of some time-1 maps of formal vector fields fixing 0, in other words, a noncommutative integral of a piecewise constant time depending formal vector field. We calculate its formal-vector-field-valued logarithm applying the Campbell–Hausdorff type formula of the Lie integral due to Chacon and Fomenko to the time depending formal vector field. For words of two time 1-maps we define Cayley diagrams in the plane spanned by the… 

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