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Award ID contains: 1832126

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  1. ; (, Journal of difference equations and applications)
    The tent map family is arguably the simplest one-parametric family of maps with non-trivial dynamics and it is still an active subject of research. In recent works, the second author, jointly with J. Yorke, studied the structural graph and backward limits of S-unimodal maps. In this article, we generalize those results to tent-like unimodal maps. By tent-like here we mean maps that share fundamental properties that characterize tent maps, namely unimodal maps without wandering intervals nor attracting periodic orbits and whose structural graph has a finite number of nodes. This article was started under grant DMS-1832126 and then completed and published under grant DMS-2308225. 
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    Free, publicly-accessible full text available March 4, 2026
  2. (, 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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  3. ; (, Nonlinear Dynamics)
    null (Ed.)
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  4. ; (, Discrete & Continuous Dynamical Systems)
    null (Ed.)
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  5. (, International Journal of Bifurcation and Chaos)
    null (Ed.)
    We study numerically the [Formula: see text]- and [Formula: see text]-limits of the Newton maps of quadratic polynomial transformations of the plane into itself. Our results confirm the conjectures posed in a recent work about the general dynamics of real Newton maps on the plane. 
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  6. ; ; ; (, Journal of Experimental and Theoretical Physics)
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  7. (, Fractals)
    We collect from several sources some of the most important results on the forward and backward limits of points under real and complex rational functions, and in particular real and complex Newton maps, in one variable and we provide numerical evidence that the dynamics of Newton maps [Formula: see text] associated to real polynomial maps [Formula: see text] with no complex roots has a complexity comparable with that of complex Newton maps in one variable. In particular such a map [Formula: see text] has no wandering domain, almost every point under [Formula: see text] is asymptotic to a fixed point and there is some non-empty open set of points whose [Formula: see text]-limit equals the set of non-regular points of the Julia set of [Formula: see text]. The first two points were proved by B. Barna in the real one-dimensional case. 
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  8. ; (, Acta Applicandae Mathematicae)
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