Groups of germs of analytic diffeomorphisms in (C^2,0)

Details Groups of germs of analytic diffeomorphisms in (C^2,0) Groups of germs of analytic diffeomorphisms in (C^2,0)

2002-07-31

arxiv.org/abs/math/0207297v1

Mathematics

Dynamical Systems

Scientific paper

Let G a group of germs of analytic diffeomorphisms in (C^2,0). We find some remarkable properties supposing that G is finite, linearizable, abelian nilpotent and solvable. In particular, if the group is abelian and has a generic dicritic diffeomorphisms, then the group is a subgroup of a 1-parametric group. In addition, we study the topological behaviour of the orbits of a dicritic diffeomorphisms. Last, we find some invariants in order to know when two diffeomorphisms are formally conjugates.

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