Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1891720 | Chaos, Solitons & Fractals | 2012 | 7 Pages |
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.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
T. Downarowicz, M. Štefánková,