On finite limit sets for transformations on the unit interval
TLDR
An infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself and the structure and order of occurrence is universal for the class.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-07-01 and is currently open access. It has received 521 citations till now. The article focuses on the topics: Limit superior and limit inferior & Limit (mathematics).read more
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Superstable credit cycles and U-sequence
TL;DR: In this paper, a particular bifurcation structure observed in the parameter space of a one-dimensional continuous piecewise smooth map generated by the credit cycle model was studied, where the map is defined over the absorbing interval via three functions, one of which is a constant.
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Periodic orbits near onset of chaos in plane Couette flow
Tobias Kreilos,Bruno Eckhardt +1 more
TL;DR: In this paper, the authors track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisisbifurcation.
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Monotonicity properties of the family of trapezoidal maps
TL;DR: In this article, it was shown that splittingrapezoidal maps according to various possible dynamical "behaviors" yields a codimension one foliation, and that aperiodic behavior is rare both from the topological and the measure theoretical point of view.
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Border-collision period-doubling scenario.
Viktor Avrutin,Michael Schanz +1 more
TL;DR: Using a one-dimensional dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, the border-collision period-doubling bifurcation scenario is investigated, and characteristic properties, like symmetry-breaking and symmetry-recovering as well as emergence of coexisting attractors and noninvariant attractive sets are investigated.
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The general exact bijective continuous solution of Feigenbaum's functional equation
TL;DR: In this paper, it was shown that, for any α ≥ 0, there are bijective solutions equivalent to translations which exist only when 0 < α < 1 and that these solutions can all be derived from continuous bijectives which are topologically equivalent to translational solutions.
References
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Non-linear transformation studies on electronic computers
P. R. Stein,Stanisław Ulam +1 more
TL;DR: In this paper, the properties of non-linear transformations in Euclidean spaces are examined, and the invariant points, finite sets, and invariant subsets of the transformations and the means for obtaining them constructively are considered.
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Eine Bemerkung über die Gruppe der topologischen Abbildungen der Kreislinie auf sich selbst
Józef Schreier,Stanislaw M. Ulam +1 more
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