Topological sequence entropy for maps of the circle

Roman Hric

Displaying similar documents to “Topological sequence entropy for maps of the circle”

Commutativity and non-commutativity of topological sequence entropy

Francisco Balibrea, Jose Salvador Cánovas Peña, Víctor Jiménez López (1999)

Annales de l'institut Fourier

Similarity:

In this paper we study the commutativity property for topological sequence entropy. We prove that if $X$ is a compact metric space and $f, g : X \to X$ are continuous maps then $h_{A} (f \circ g) = h_{A} (g \circ f)$ for every increasing sequence $A$ if $X = [0, 1]$ , and construct a counterexample for the general case. In the interim, we also show that the equality $h_{A} (f) = h_{A} (f |_{\cap_{n \geq 0} f^{n} (X)})$ is true if $X = [0, 1]$ but does not necessarily hold if $X$ is an arbitrary compact metric space.

Topological entropy of Cournot-Puu duopoly.

Cánovas, Jose S., Medina, David López (2010)

Discrete Dynamics in Nature and Society

Similarity:

Distributional chaos on tree maps: the star case

Jose S. Cánovas (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $𝕏 = {z \in ℂ : z^{n} \in [0, 1]}$ , $n \in ℕ$ , and let $f : 𝕏 \to 𝕏$ be a continuous map having the branching point fixed. We prove that $f$ is distributionally chaotic iff the topological entropy of $f$ is positive.