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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Journal ArticleDOI
Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li—Yorke
M. Howard Lee,M. Howard Lee +1 more
TL;DR: In this article, the fixed points of 3-cycle are obtained analytically by solving a sextic equation, and a fixed point spectrum is obtained from the Sharkovskii limit.
Book ChapterDOI
Prologue Some ideas about strange attractors
L. Garrido,C. Simó +1 more
TL;DR: For two-dimensional diffeomorphisms or flows reducing essentially to them the evolution of S.A. can be described geometrically using bifurcations, homoclinic and heterocalic points as discussed by the authors.
Journal ArticleDOI
Symbolic dynamics of the sine-square map
Fa-geng Xie,Bailin Hao +1 more
TL;DR: In this paper, the skeleton of superstable orbits in the kneading plane has been constructed using a hybrid optical bistability device with liquid crystal as the nonlinear medium in the cavity.
Journal ArticleDOI
Distribution of iterates of first order difference equations
TL;DR: In this article, an invariant measure which is continuous with respect to Lebesgue measure is constructed for a particular first order difference equation that has an extensive biological pedigree, which gives the density of the population whose growth is governed by the difference equation.
Journal ArticleDOI
Phase-length distributions in intermittent band switching
TL;DR: In this article, the distribution of phase lengths t for intermittent band switching is investigated and its form is observed to deviate from a exponential function; a minimal phase length is seen to exist and the probabilities for the first few occuring phase lengths are often strongly enhanced or suppressed.
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.
Journal ArticleDOI
Eine Bemerkung über die Gruppe der topologischen Abbildungen der Kreislinie auf sich selbst
Józef Schreier,Stanislaw M. Ulam +1 more
Journal ArticleDOI