On the classification of inverse limits of tent maps

Volume 187 / 2005

Louis Block, Slagjana Jakimovik, Lois Kailhofer, James Keesling Fundamenta Mathematicae 187 (2005), 171-192 MSC: Primary 54F15; Secondary 37E05, 37B45. DOI: 10.4064/fm187-2-5

Abstract

Let $f_s$ and $f_t$ be tent maps on the unit interval. In this paper we give a new proof of the fact that if the critical points of $f_s$ and $f_t$ are periodic and the inverse limit spaces $(I,f_s)$ and $(I,f_t)$ are homeomorphic, then $s = t$. This theorem was first proved by Kailhofer. The new proof in this paper simplifies the proof of Kailhofer. Using the techniques of the paper we are also able to identify certain isotopies between homeomorphisms on the inverse limit space.

Authors

  • Louis BlockDepartment of Mathematics
    University of Florida
    Gainesville, FL 32611-8105, U.S.A.
    e-mail
  • Slagjana JakimovikDepartment of Mathematics
    Cyril and Methodius University
    1000 Skopje, Macedonia
    e-mail
  • Lois KailhoferDepartment of Mathematics
    Alverno College
    Milwaukee, WI 53215, U.S.A.
    e-mail
  • James KeeslingDepartment of Mathematics
    University of Florida
    Gainesville, FL 32611-8105, U.S.A.
    e-mail

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