Displaying similar documents to “Dense chaos”

Characterization of ω -limit sets of continuous maps of the circle

David Pokluda (2002)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we extend results of Blokh, Bruckner, Humke and Sm’ıtal [Trans. Amer. Math. Soc. (1996), 1357–1372] about characterization of ω -limit sets from the class 𝒞 ( I , I ) of continuous maps of the interval to the class 𝒞 ( 𝕊 , 𝕊 ) of continuous maps of the circle. Among others we give geometric characterization of ω -limit sets and then we prove that the family of ω -limit sets is closed with respect to the Hausdorff metric.

The converse problem for a generalized Dhombres functional equation

L. Reich, Jaroslav Smítal, M. Štefánková (2005)

Mathematica Bohemica

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We consider the functional equation f ( x f ( x ) ) = ϕ ( f ( x ) ) where ϕ J → J is a given homeomorphism of an open interval J ⊂ ( 0 , ∞ ) and f ( 0 , ∞ ) → J is an unknown continuous function. A characterization of the class 𝒮 ( J , ϕ ) of continuous solutions f is given in a series of papers by Kahlig and Smítal 1998–2002, and in a recent paper by Reich et al. 2004, in the case when ϕ is increasing. In the present paper we solve the converse problem, for which continuous maps f ( 0 , ∞ ) → J , where J is an interval, there is an increasing homeomorphism ϕ of J such...