Chaos on hyperspaces
Result description
Let f be a continuous self-map of a compact metric space X. The transformation f induces in a natural way a self-map F defined on the hyperspace K(X) of all nonempty closed subsets of X. We study which of the most usual notions of chaos for dynamical systems induced by f are inherited by F and vice versa. We consider distributional chaos, Li-Yorke chaos, omega-chaos, Devaney chaos, topological chaos, specification property and their variants.
Keywords
distributional chaosLi?Yorke chaosomega-chaosDevaney chaostopological chaosspecification property
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Chaos on hyperspaces
Original language description
Let f be a continuous self-map of a compact metric space X. The transformation f induces in a natural way a self-map F defined on the hyperspace K(X) of all nonempty closed subsets of X. We study which of the most usual notions of chaos for dynamical systems induced by f are inherited by F and vice versa. We consider distributional chaos, Li-Yorke chaos, omega-chaos, Devaney chaos, topological chaos, specification property and their variants.
Czech name
Chaos na hyperprostoru
Czech description
Buď f spojité zobrazení kompaktního metrického prostoru X. Zobrazení f indukuje přizoreným způsobem zobrazení F na hyperprostoru K(X) všech neprázdných uzavřených podmnožin X. Studujeme, které z běžně používaných definic chaosu dynamického systému (X,f)je přenášena na (K(X),F) a naopak. Konstruujeme distribuční chaos, Li-Yorke chaos, omega-chaos, Devaney chaos, topologický chaos, specifikační vlastnost.
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinear Analysis: Theory, Methods & Applications
ISSN
0362-546X
e-ISSN
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Volume of the periodical
71
Issue of the periodical within the volume
1-2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
8
Pages from-to
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UT code for WoS article
000266225600001
EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2009