Chaos for multivalued maps and induced hyperspace maps

Jan Andres

Chaos, Solitons & Fractals, 2020, vol. 138, issue C

Abstract: Let (X, d) be a compact metric space and φ: X⊸X be a multivalued map. At first, we will extend for these maps the notions of a topological entropy and Robinson’s chaos from a single-valued into a multivalued setting and show their basic properties. Then, for a subclass of multivalued continuous maps with compact values, we will clarify their relationship to the induced (hyper)maps φ*:K(X)→K(X) in the hyperspace (K(X),dH), endowed with the Hausdorff metric dH, where K(X) consists of all compact subsets of X. Concretely, we will show that a positive topological entropy h(φ) of φ implies a positive topological entropy h(φ*) of φ*. On the other hand, Robinson’s chaos to φ* implies in a reverse way Robinson’s chaos to φ.

Keywords: Topological entropy; Robinson’s chaos; multivalued maps; hyperspace; induced hypermaps; forcing properties (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077920302988
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:138:y:2020:i:c:s0960077920302988

DOI: 10.1016/j.chaos.2020.109898

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. ().