Stability of the ω-limit set for unimodal transformations

Consider the map T omega(T) on the collection of unimodal transformations, where omega(T) is the omega-limit set of T. The collection of unimodal transformations is endowed with the topology of uniform convergence, and the collection of subsets of [0, 1] is endowed with the Hausdorff metric. Conditi...

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Bibliographic Details
Published in:Nonlinearity 2009-05, Vol.22 (5), p.955-966
Main Authors: Hofbauer, Franz, Raith, Peter
Format: Article
Language:English
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Summary:Consider the map T omega(T) on the collection of unimodal transformations, where omega(T) is the omega-limit set of T. The collection of unimodal transformations is endowed with the topology of uniform convergence, and the collection of subsets of [0, 1] is endowed with the Hausdorff metric. Conditions on a unimodal transformation T implying the continuity of the map S omega(S) at T are investigated.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/22/5/002