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Dynamics of piecewise contractions of the interval



We study the long-term behavior of injective piecewise contractions of the interval. We prove that every injective piecewise contraction with $n-1$ discontinuities has at most $n$ periodic orbits and is topologically conjugate to a piecewise linear contraction.



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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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