Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two
Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 51-61
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
hereditarily decomposable continuum, logistic mapping, inverse limit
Affiliations des auteurs :
W. Ingram 1 ; Robert Roe 1
@article{10_4064_cm_81_1_51_61,
author = {W. Ingram and Robert Roe},
title = {Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two},
journal = {Colloquium Mathematicum},
pages = {51--61},
year = {1999},
volume = {81},
number = {1},
doi = {10.4064/cm-81-1-51-61},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-81-1-51-61/}
}
TY - JOUR AU - W. Ingram AU - Robert Roe TI - Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two JO - Colloquium Mathematicum PY - 1999 SP - 51 EP - 61 VL - 81 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-81-1-51-61/ DO - 10.4064/cm-81-1-51-61 LA - en ID - 10_4064_cm_81_1_51_61 ER -
%0 Journal Article %A W. Ingram %A Robert Roe %T Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two %J Colloquium Mathematicum %D 1999 %P 51-61 %V 81 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/cm-81-1-51-61/ %R 10.4064/cm-81-1-51-61 %G en %F 10_4064_cm_81_1_51_61
W. Ingram; Robert Roe. Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two. Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 51-61. doi: 10.4064/cm-81-1-51-61
Cité par Sources :