TITLE

Families, filters and chaos

AUTHOR(S)
Oprocha, Piotr
PUB. DATE
August 2010
SOURCE
Bulletin of the London Mathematical Society;Aug2010, Vol. 42 Issue 4, p713
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we use the definition of (ℱ1, ℱ2)-chaos introduced recently by Tan and Xiong together with the properties of residual relations as a tool in construction of various kinds of scrambled sets. In particular, we show that a continuous map acting on a compact metric space has an ɛ-scrambled set if and only if it has a distributionally ɛ-scrambled set with respect to a sequence. We also provide an example of a topologically mixing map with positive topological entropy but without DC1 pairs.
ACCESSION #
52348029

 

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