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
Citations
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Chaotic behaviour of fluidized-bed catalytic reactors with consecutive exothermic chemical reactions
TL;DR: In this paper, a two-phase model for the nonisothermal fluidized-bed catalytic reactor with consecutive exothermic reactions has been used to investigate the bifurcation, instability and chaotic characteristics of this unit.
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Cyclic star products and universalities in symbolic dynamics of trimodal maps
Zhong Zhou,Shou-Li Peng +1 more
TL;DR: In this paper, the authors generalized Feigenbaum's metric universalities in unimodal maps to trimodal map and obtained four equal-value universal convergent rates and three universal scaling factors.
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Dynamics of simple one-dimensional maps under perturbation
TL;DR: In this paper, the authors studied the dynamics exhibited by some of these simple one-dimensional maps under constant perturbations and showed that the differences in their behaviour under perturbation need to be taken into consideration before using them for modelling any real process.
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The existence of periodic orbits of the tent map
TL;DR: For the tent map Tμ(x) = μx for 0 ⩽ x⩽ 1 2 and = μ(1 − x) for 1 2 ⩻ x ⩾ 1, the μ values are determined for which periodic orbits of each order exist Except for period 2n orbits which exist for all μ ⩲ 1, the Sarkovskii ordering is vividly illustrated as discussed by the authors.
References
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Book
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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