"Mobius transformations with n-cycles "geometric viewpoint
BLEL, TARIQ A. Al-FADHEL and MONGI . 2013
Let M be the group of Mobius transformations on the extented plane and
f_M={f^n, n in Z} the cyclic subgroup of M generated by f , for f in M. If f_M is
finite of order n, f is called an n-cycle. We prove in the first part that if f is an n-cycle,
then for any a in the extented plane, the orbit of f lies on a circle. Furthermore we
characterize with geometric arguments the circles which are invariant under this kind of
transformations.
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