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We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-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.
Chris Good, and Brian E. Raines. "Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets." Fundamenta Mathematicae 191.1 (2006): 1-21. <http://eudml.org/doc/282716>.
@article{ChrisGood2006, abstract = {We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-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.}, author = {Chris Good, Brian E. Raines}, journal = {Fundamenta Mathematicae}, keywords = {attractor; invariant set; inverse limits; unimodal; continuum; indecomposable}, language = {eng}, number = {1}, pages = {1-21}, title = {Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets}, url = {http://eudml.org/doc/282716}, volume = {191}, year = {2006}, }
TY - JOUR AU - Chris Good AU - Brian E. Raines TI - Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets JO - Fundamenta Mathematicae PY - 2006 VL - 191 IS - 1 SP - 1 EP - 21 AB - We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-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. LA - eng KW - attractor; invariant set; inverse limits; unimodal; continuum; indecomposable UR - http://eudml.org/doc/282716 ER -