Shift spaces and attractors in noninvertible horseshoes

@article{Bothe1997,
abstract = {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.},
author = {Bothe, H.},
journal = {Fundamenta Mathematicae},
keywords = {horseshoes; noninvertible maps; shift spaces; attractors},
language = {eng},
number = {3},
pages = {267-289},
title = {Shift spaces and attractors in noninvertible horseshoes},
url = {http://eudml.org/doc/212211},
volume = {152},
year = {1997},
}

TY - JOUR
AU - Bothe, H.
TI - Shift spaces and attractors in noninvertible horseshoes
JO - Fundamenta Mathematicae
PY - 1997
VL - 152
IS - 3
SP - 267
EP - 289
AB - 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.
LA - eng
KW - horseshoes; noninvertible maps; shift spaces; attractors
UR - http://eudml.org/doc/212211
ER -