A classification of inverse limit spaces of tent maps with periodic critical points

Lois Kailhofer. "A classification of inverse limit spaces of tent maps with periodic critical points." Fundamenta Mathematicae 177.2 (2003): 95-120. <http://eudml.org/doc/283300>.

@article{LoisKailhofer2003,
abstract = {We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps $f_a$, $f_b$ with periodic critical points, we show that the inverse limit spaces $(_a,f_a)$ and $(_b,g_b)$ are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.},
author = {Lois Kailhofer},
journal = {Fundamenta Mathematicae},
keywords = {compact metric spaces; inverse limit space; tent maps},
language = {eng},
number = {2},
pages = {95-120},
title = {A classification of inverse limit spaces of tent maps with periodic critical points},
url = {http://eudml.org/doc/283300},
volume = {177},
year = {2003},
}

TY - JOUR
AU - Lois Kailhofer
TI - A classification of inverse limit spaces of tent maps with periodic critical points
JO - Fundamenta Mathematicae
PY - 2003
VL - 177
IS - 2
SP - 95
EP - 120
AB - We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps $f_a$, $f_b$ with periodic critical points, we show that the inverse limit spaces $(_a,f_a)$ and $(_b,g_b)$ are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.
LA - eng
KW - compact metric spaces; inverse limit space; tent maps
UR - http://eudml.org/doc/283300
ER -