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Creators/Authors contains: "Roberto De Leo"

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  1. (, International journal of bifurcation and chaos in applied sciences and engineering)
    While the forward trajectory of a point in a discrete dynamical system is always unique, in general, a point can have infinitely many backward trajectories. The union of the limit points of all backward trajectories through x was called by Hero the “special α-limit” (sα-limit for short) of x. In this article, we show that there is a hierarchy of sα-limits of points under iterations of a S-unimodal map: the size of the sα-limit of a point increases monotonically as the point gets closer and closer to the attractor. The sα-limit of any point of the attractor is the whole nonwandering set. This hierarchy reflects the structure of the graph of a S-unimodal map recently introduced jointly by Jim Yorke and the present author. 
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