Dense chaos

Ľubomír Snoha

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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 $ϕ J \to J$ is a given homeomorphism of an open interval $J \subset (0, \infty)$ and $f (0, \infty) \to J$ 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 $f (0, \infty) \to J$ , where $J$ is an interval, there is an increasing homeomorphism $ϕ$ of $J$ such...

Displaying similar documents to “Dense chaos”

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

The converse problem for a generalized Dhombres functional equation

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