Ponencia
Skew-product maps with base having closed set of periodic points
Autor/es | García Guirao, Juan Luis
López Guerrero, Miguel Ángel |
Fecha de publicación | 2007-09 |
Fecha de depósito | 2016-02-18 |
Publicado en |
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Resumen | In [Proc. ECIT-89, World Scientific, (1991), 177–183], A. N. Sharkovski˘ı and S.F. Kolyada stated the problem of characterization skew-product maps having zero topological entropy. It is known that, even under some additional ... In [Proc. ECIT-89, World Scientific, (1991), 177–183], A. N. Sharkovski˘ı and S.F. Kolyada stated the problem of characterization skew-product maps having zero topological entropy. It is known that, even under some additional assumptions, this aim has not been reached. In [J. Math. Anal. Appl., 287, (2003), 516–521], J. L. G. Guirao and J. Chudziak partially solved the problem in the class of skew-product maps with base map having closed set of periodic points. The present paper has two aims for this class of maps, on one hand to improve that solution showing the equivalence between the property “to have zero topological entropy” and the fact “not to be Li-Yorke chaotic in the union of the ω-limit sets of recurrent points”. On other hand, we show that the properties “to have closed set of periodic points” and “all nonwandering points are periodic” are not mutually equivalent properties, for doing this we disprove a result from Efremova of 1990. |
Cita | García Guirao, J.L. y López Guerrero, M.Á. (2007). Skew-product maps with base having closed set of periodic points. |
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