Geodesic
Continuum many tent map inverse limits with homeomorphic postcritical $\omega $-limit sets
Chris Good 1   ; Brian E. Raines 2
1 School of Mathematics and Statistics University of Birmingham Birmingham, B15 2TT, UK
2 Department of Mathematics Baylor University Waco, TX 76798-7328, U.S.A.
Fundamenta Mathematicae, Tome 191 (2006) no. 1, pp. 1-21 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical $\omega $-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.
DOI : 10.4064/fm191-1-1
Keywords: demonstrate set topologically distinct inverse limit spaces tent maps cantor set its postcritical omega limit set has cardinality continuum set folding points points which space homeomorphic product zero dimensional set arc each these spaces cantor set

Chris Good  1   ; Brian E. Raines  2

1 School of Mathematics and Statistics University of Birmingham Birmingham, B15 2TT, UK
2 Department of Mathematics Baylor University Waco, TX 76798-7328, U.S.A. 
@article{10_4064_fm191_1_1,
     author = {Chris Good and Brian E. Raines},
     title = {Continuum many tent map inverse limits with
 homeomorphic postcritical $\omega $-limit sets},
     journal = {Fundamenta Mathematicae},
     pages = {1--21},
     year = {2006},
     volume = {191},
     number = {1},
     doi = {10.4064/fm191-1-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm191-1-1/}
}
TY  - JOUR
AU  - Chris Good
AU  - Brian E. Raines
TI  - Continuum many tent map inverse limits with
 homeomorphic postcritical $\omega $-limit sets
JO  - Fundamenta Mathematicae
PY  - 2006
SP  - 1
EP  - 21
VL  - 191
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm191-1-1/
DO  - 10.4064/fm191-1-1
LA  - en
ID  - 10_4064_fm191_1_1
ER  - 
%0 Journal Article
%A Chris Good
%A Brian E. Raines
%T Continuum many tent map inverse limits with
 homeomorphic postcritical $\omega $-limit sets
%J Fundamenta Mathematicae
%D 2006
%P 1-21
%V 191
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/fm191-1-1/
%R 10.4064/fm191-1-1
%G en
%F 10_4064_fm191_1_1
Chris Good; Brian E. Raines. Continuum many tent map inverse limits with
 homeomorphic postcritical $\omega $-limit sets. Fundamenta Mathematicae, Tome 191 (2006) no. 1, pp. 1-21. doi: 10.4064/fm191-1-1

Cité par Sources :