Iteration of the power operation

This thesis is an investigation of the sequence of functions defined by fl (x) -xand fn+1 (x) -x , where the power is the principal value.In the case where the sequence is restricted to positive real this sequence of functions over thecomplex plane, we attack real numbers, the problem yields to the methods of analysis and we prove the behavior of the sequence.The more general problem of describing the behavior of both analytically and numerically. Though no full rigorous solution is given, the results presented suggest the behavior of the sequence over the complex plane is very interesting.