On open problems concerning distributional chaos for triangular maps
Result description
We show that in the class T of the triangular maps (x, y) bar right arrow (f(x), g(x)(y)) of the square there is a map of type 2(infinity) with non-minimal recurrent points which is not DC3. We also show that every DC1 continuous map of a compact metricspace has a trajectory which cannot be (weakly) approximated by trajectories of compact periodic sets. These two results make possible to answer some open questions concerning classification of maps in T with zero topological entropy, and contribute to an old problem formulated by A.N. Sharkovsky.
Keywords
Distributional chaosTriangular mapsMinimal setRecurrent pointsTopological entropy
The result's identifiers
Result code in IS VaVaI
Result on the web
http://www.sciencedirect.com/science/article/pii/S0362546X11005347
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On open problems concerning distributional chaos for triangular maps
Original language description
We show that in the class T of the triangular maps (x, y) bar right arrow (f(x), g(x)(y)) of the square there is a map of type 2(infinity) with non-minimal recurrent points which is not DC3. We also show that every DC1 continuous map of a compact metricspace has a trajectory which cannot be (weakly) approximated by trajectories of compact periodic sets. These two results make possible to answer some open questions concerning classification of maps in T with zero topological entropy, and contribute to an old problem formulated by A.N. Sharkovsky.
Czech name
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Czech description
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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
2011
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
74
Issue of the periodical within the volume
18
Country of publishing house
GB - UNITED KINGDOM
Number of pages
5
Pages from-to
7342-7346
UT code for WoS article
000295714200044
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
2011