On the continuity of global attractors

Luan T. Hoang, Eric J. Olson, James C. Robinson

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Let Λ be a complete metric space, and let {Sλ(·) : λ ∈ Λ} be a parametrised family of semigroups with global attractors Aλ. We assume that there exists a fixed bounded set D such that Aλ ⊂ D for every λ ∈ Λ. By viewing the attractors as the limit as t → ∞ of the sets Sλ(t)D, we give simple proofs of the equivalence of ‘equi-attraction’ to continuity (when this convergence is uniform in λ) and show that the attractors Aλ are continuous in λ at a residual set of parameters in the sense of Baire Category (when the convergence is only pointwise).

Original languageEnglish
Pages (from-to)4389-4395
Number of pages7
JournalProceedings of the American Mathematical Society
Volume143
Issue number10
DOIs
StatePublished - Oct 1 2015

Keywords

  • Baire one function
  • Continuity
  • Dini’s Theorem
  • Equi-attraction
  • Global attractor

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