Geodesic
Shift spaces and attractors in noninvertible horseshoes
Fundamenta Mathematicae, Tome 152 (1997) no. 3, pp. 267-289.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

As is well known, a horseshoe map, i.e. a special injective reimbedding of the unit square $I^2$ in $ℝ^2$ (or more generally, of the cube $I^m$ in $ℝ^m$) as considered first by S. Smale [5], defines a shift dynamics on the maximal invariant subset of $I^2$ (or $I^m$). It is shown that this remains true almost surely for noninjective maps provided the contraction rate of the mapping in the stable direction is sufficiently strong, and bounds for this rate are given.
DOI : 10.4064/fm-152-3-267-289
Keywords: horseshoes, noninvertible maps, shift spaces, attractors

H. G. Bothe 1

1 
@article{10_4064_fm_152_3_267_289,
     author = {H. G. Bothe},
     title = {Shift spaces and attractors in noninvertible horseshoes},
     journal = {Fundamenta Mathematicae},
     pages = {267--289},
     publisher = {mathdoc},
     volume = {152},
     number = {3},
     year = {1997},
     doi = {10.4064/fm-152-3-267-289},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-152-3-267-289/}
}
TY  - JOUR
AU  - H. G. Bothe
TI  - Shift spaces and attractors in noninvertible horseshoes
JO  - Fundamenta Mathematicae
PY  - 1997
SP  - 267
EP  - 289
VL  - 152
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-152-3-267-289/
DO  - 10.4064/fm-152-3-267-289
LA  - en
ID  - 10_4064_fm_152_3_267_289
ER  - 
%0 Journal Article
%A H. G. Bothe
%T Shift spaces and attractors in noninvertible horseshoes
%J Fundamenta Mathematicae
%D 1997
%P 267-289
%V 152
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-152-3-267-289/
%R 10.4064/fm-152-3-267-289
%G en
%F 10_4064_fm_152_3_267_289
H. G. Bothe. Shift spaces and attractors in noninvertible horseshoes. Fundamenta Mathematicae, Tome 152 (1997) no. 3, pp. 267-289. doi : 10.4064/fm-152-3-267-289. http://geodesic.mathdoc.fr/articles/10.4064/fm-152-3-267-289/

Cité par Sources :