Coherent lists and chaotic sets

Piotr Oprocha

doi:10.3934/dcds.2011.31.797

Article Contents

2011, Volume 31, Issue 3: 797-825. Doi: 10.3934/dcds.2011.31.797

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Coherent lists and chaotic sets

Piotr Oprocha^1,

1.
Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków

Received: April 2010

Revised: July 2011

Published: September 2011

Abstract / Introduction Related Papers Cited by

Abstract

In this article we apply (recently extended by Kato and Akin) an elegant method of Iwanik (which adopts independence relations of Kuratowski and Mycielski) in the construction of various chaotic sets. We provide ''easy to track'' proofs of some known facts and establish new results as well. The main advantage of the presented approach is that it is easy to verify each step of the proof, when previously it was almost impossible to go into all the details of the construction (usually performed as an inductive procedure). Furthermore, we are able extend known results on chaotic sets in an elegant way. Scrambled, distributionally scrambled and chaotic sets with relation to various notions of mixing are considered.

Keywords:

Mathematics Subject Classification: Primary: 37B05; Secondary: 37D45.

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