A+ CATEGORY SCIENTIFIC UNIT

Continuum many tent map inverse limits with homeomorphic postcritical $\omega $-limit sets

Volume 191 / 2006

Chris Good, Brian E. Raines 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.

Authors

  • Chris GoodSchool of Mathematics and Statistics
    University of Birmingham
    Birmingham, B15 2TT, UK
    e-mail
  • Brian E. RainesDepartment of Mathematics
    Baylor University
    Waco, TX 76798-7328, U.S.A.
    e-mail

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