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aequationes mathematicae

, Volume 57, Issue 2–3, pp 303–311 | Cite as

Topological transitivity for expanding piecewise monotonic maps on the interval

  • P. Raith

Summary.

Let T : [0, 1] → [0, 1] be an expanding piecewise monotonic map. Conditions on T and \( {\rm inf}_{x\in [0,1]}|T^{\prime}x| \) implying the topological transitivity of T are investigated. For a monotonic mod one transformation T topological transitivity is obtained, if \( {\rm inf}_{x\in [0,1]}|T^{\prime}x| > 2 \). If T is a monotonic mod one transformation with three monotonic pieces, then \( {\rm inf}_{x\in [0,1]}|T^{\prime}x| \geq 2 \) implies the topological transitivity of T. An expanding monotonic mod one transformation T with lim x → 0+ T x = 0 or lim x → 1 - T x = 1 is topologically transitive.

Keywords. Piecewise monotonic map, topological transitivity, expanding map, mod one transformation, Markov diagram. 

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Copyright information

© Birkhäuser Verlag, Basel, 1999

Authors and Affiliations

  • P. Raith
    • 1
  1. 1.Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria, e-mail: Peter.Raith@univie.ac.atAT

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