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

T. Downarowicz and M. Štefánková

Chaos, Solitons & Fractals, 2012, vol. 45, issue 12, 1566-1572

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:45:y:2012:i:12:p:1566-1572

DOI: 10.1016/j.chaos.2012.09.005

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