Sign in
Back
ON INVARIANT epsilon-SCRAMBLED SETS
Journal article   Peer reviewed

ON INVARIANT epsilon-SCRAMBLED SETS

Francisco Balibrea, Juan L. G. Guirao and Piotr Oprocha
International journal of bifurcation and chaos in applied sciences and engineering, Vol.20(9), pp.2925-2935
09/2010
DOI: https://doi.org/10.1142/S0218127410027465

Abstract

Mathematics Mathematics, Interdisciplinary Applications Multidisciplinary Sciences Physical Sciences Science & Technology Science & Technology - Other Topics
This article is devoted to the study of invariant epsilon-scrambled sets. We show that every topologically mixing map with at least one fixed point contains at least one such set. Additionally we show that this condition can be weakened in the case of symbolic dynamics, e.g. mixing can be replaced by transitivity. Some relations between mixing and proximal relation are also studied.

Metrics

1 Record Views

Details