On negative limit sets for one-dimensional dynamics
Result description
In this paper we study the structure of negative limit sets of maps on the unit interval. We prove that every alpha-limit set is an omega-limit set, while the converse is not true in general. Surprisingly, it may happen that the space of all alpha-limitsets of interval maps is not closed in the Hausdorff metric (and thus some omega-limit sets are never obtained as alpha-limit sets). Moreover, we prove that the set of all recurrent points is closed if and only if the space of all alpha-limit sets is closed.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/61989100:27240/12:86082566 RIV/61989100:27740/12:86082566
Result on the web
http://www.sciencedirect.com/science/article/pii/S0362546X11008510
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On negative limit sets for one-dimensional dynamics
Original language description
In this paper we study the structure of negative limit sets of maps on the unit interval. We prove that every alpha-limit set is an omega-limit set, while the converse is not true in general. Surprisingly, it may happen that the space of all alpha-limitsets of interval maps is not closed in the Hausdorff metric (and thus some omega-limit sets are never obtained as alpha-limit sets). Moreover, we prove that the set of all recurrent points is closed if and only if the space of all alpha-limit sets is closed.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2012
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
75
Issue of the periodical within the volume
6
Country of publishing house
GB - UNITED KINGDOM
Number of pages
6
Pages from-to
3262-3267
UT code for WoS article
000300191000023
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
2012