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## Colloquium Mathematicum

1999 | 81 | 1 | 51-61
Tytuł artykułu

### Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We derive several properties of unimodal maps having only periodic points whose period is a power of 2. We then consider inverse limits on intervals using a single strongly unimodal bonding map having periodic points whose only periods are all the powers of 2. One such mapping is the logistic map, $f_λ(x)$ = 4λx(1-x) on [f(λ),λ], at the Feigenbaum limit, λ ≈ 0.89249. It is known that this map produces an hereditarily decomposable inverse limit with only three topologically different subcontinua. Other examples of such maps are given and it is shown that any two strongly unimodal maps with periodic point whose only periods are all the powers of 2 produce homeomorphic inverse limits whenever each map has the additional property that the critical point lies in the closure of the orbit of the right endpoint of the interval.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
51-61
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-08-27
poprawiono
1998-12-21
Twórcy
autor
• Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65401, U.S.A.
autor
• Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65401, U.S.A.
Bibliografia
• [1] M. Barge and W. T. Ingram, Inverse limits on [0,1] using logistic maps as bonding maps, Topology Appl. 72 (1996), 159-172.
• [2] P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Basel, 1980.
• [3] R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Benjamin, Menlo Park, 1986.
• [4] W. T. Ingram, Periodicity and indecomposability, Proc. Amer. Math. Soc. 123 (1995), 1907-1916.
• [5] Z. Nitecki, Topological dynamics on the interval, in: Ergodic Theory and Dynamical Systems II, A. Katok (ed.), Birkhäuser, Boston, 1982, 1-73.
Typ dokumentu
Bibliografia
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