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Spreadsheet-based Approach to Mapping a Segment into Itself The problem of mapping a segment into itself that will be discussed in this section in connection with the behavior of orbits defi ned by equation (6) is a special case of a more general problem of mapping the circle into itself. In the specifi c case of phase-locked loops, this more general problem was studied in [39,40,7]. Whereas a spreadsheet’s computational capability allows for the representation of problems involving complex variables by dealing separately with real and imaginary parts [5,10], in what follows the discussion will be limited to a spreadsheet-based demonstration of what it means for the segment to be mapped into itself.