absence of the asymptotic stability of the attractor, implying that the attractor would presumably be an “SNA”.

In the following, we try to illustrate outline of the algorithm in the form of a pseudo program.


    global variables (for parameters): 
      Iinit: a segment on the initial fiber
        chosen so that any invariant set has
        non empty intersection with this segment)
      TList: set of integer
        used to specify theta values of fibers to
        be observed

    global variables (for results):
      InvList: set of segments
        list of pull-back attractor of the
        segment map on the target fiber of Part1
      Unity[J] (J: a member of InvList): boolean
        true if the invariant set represented
        by J do not have proper subset which is
        an attracting invariant set
      RepellerImage[J,t]
        (J: a member of InvList,
         t: a member of TList): set of segments 
        image of a section of repeller
        whose basin of repulsion corresponds to J
      SNA[J] (J : a member of InvList):  boolean
        true if J is classified as SNA

    working variables:
      I*,J*,K*: segments on a fiber
        I*:  on initial fiber
        J*:  on target fiber
        K*:  on future fiber

#### Part 1: Search for the attracting sets of $\tilde M$

    Part1Main
     clear InvList
     call P1CheckImage(Iinit)

    Procedure P1CheckImage(I)
      