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Stability of the ω-limit set for unimodal transformations

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Published 26 March 2009 • 2009 IOP Publishing Ltd and London Mathematical Society
, , Citation Franz Hofbauer and Peter Raith 2009 Nonlinearity 22 955 DOI 10.1088/0951-7715/22/5/002

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1 Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria

Dates

  1. Received 10 July 2008
  2. Published

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Abstract

Consider the map T ↦ ω(T) on the collection of unimodal transformations, where ω(T) is the ω-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 ↦ ω(S) at T are investigated.

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10.1088/0951-7715/22/5/002