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Embedding Toeplitz systems in triangular maps: The last but one problem of the Sharkovsky classification program

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  • Downarowicz, T.
  • Štefánková, M.

Abstract

We give an example of a triangular map of the unit square containing a minimal Li–Yorke chaotic set and such that, in the whole system, there are no DC3-pairs. This solves the last but one problem of the Sharkovsky program of classification of triangular maps. We use completely new methods, in fact we show that every zero-dimensional almost 1–1 extension of the dyadic odometer can be realized as the unique nonperiodic minimal set in a triangular map of type 2∞. In case of a regular Toeplitz system we can additionally arrange that all invariant measures are supported by minimal sets.

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  • Downarowicz, T. & Štefánková, M., 2012. "Embedding Toeplitz systems in triangular maps: The last but one problem of the Sharkovsky classification program," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1566-1572.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:12:p:1566-1572
    DOI: 10.1016/j.chaos.2012.09.005
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    References listed on IDEAS

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    1. Balibrea, F. & Smı́tal, J. & Štefánková, M., 2005. "The three versions of distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1581-1583.
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    Cited by:

    1. Downarowicz, Tomasz, 2013. "Minimal subsystems of triangular maps of type 2∞; Conclusion of the Sharkovsky classification program," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 61-71.

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