Continuum many tent map inverse limits with homeomorphic postcritical $\omega $-limit sets
Volume 191 / 2006
Fundamenta Mathematicae 191 (2006), 1-21
MSC: 37B45, 37E05, 54F15, 54H20.
DOI: 10.4064/fm191-1-1
Abstract
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.
