"Mobius transformations with n-cycles "geometric viewpoint

Journal Article

BLEL, TARIQ A. Al-FADHEL and MONGI . 2013

• نوع عمل المنشور: theoric
• المجلة \ الصحيفة: ARAB JOURNAL OF MATHEMATICAL SCIENCES
• رقم العدد: 1
• رقم الإصدار السنوي: (Arab J Math Sci 19(1) (2013
• الصفحات: 21-34

مستخلص المنشور

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.