Maximal Abelian Torsion Subgroups of Diff(C,0)

Details Maximal Abelian Torsion Subgroups of Diff(C,0) Maximal Abelian Torsion Subgroups of Diff(C,0)

2009-03-13

arxiv.org/abs/0903.2396v1

Mathematics

Dynamical Systems

Scientific paper

In the study of the local dynamics of a germ of diffeomorphism fixing the origin in C, an important problem is to determine the centralizer of the germ in the group Diff(C,0) of germs of diffeomorphisms fixing the origin. When the germ is not of finite order, then the centralizer is abelian, and hence a maximal abelian subgroup of Diff(C,0). Conversely any maximal abelian subgroup which contains an element of infinite order is equal to the centralizer of that element. A natural question is whether every maximal abelian subgroup contains an element of infinite order, or whether there exist maximal abelian torsion subgroups; we show that such subgroups do indeed exist, and moreover that any infinite subgroup of the rationals modulo the integers Q/Z can be embedded into Diff(C,0) as such a subgroup.

Affiliated with

Also associated with

No associations

Rating

Maximal Abelian Torsion Subgroups of Diff(C,0) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Maximal Abelian Torsion Subgroups of Diff(C,0), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Maximal Abelian Torsion Subgroups of Diff(C,0) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-228903