Set-valued discrete chaos

Alfredo Peris

Chaos, Solitons & Fractals, 2005, vol. 26, issue 1, 19-23

Abstract: Given a continuous map f:X→X on a metric space (X,d), we characterize topological transitivity for the (set-valued) map f¯:K(X)→K(X) induced by f on the space K(X) of compact subsets of X, endowed with the Hausdorff distance. More precisely, f¯ is transitive if and only if f is weakly mixing. Some consequences are also derived for the dynamics on fractals and for (continuous and) linear maps on infinite-dimensional spaces.

Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077905000627
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:26:y:2005:i:1:p:19-23

DOI: 10.1016/j.chaos.2004.12.039

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().