Abstract
ABSTRACT We investigate the Möbius groups theory in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. In this paper, we first generalize classical conjugacy classification to bicomplex analysis. Then we have a discussion of the iterates of a bicomplex Möbius transformation and study the attractive and repulsive fixed points in bicomplex setting. Finally, we shall prove two useful results concerning fixed point.
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