Displaying similar documents to “Topological conjugacies of piecewise monotone interval maps.”

Transitive sensitive subsystems for interval maps

Sylvie Ruette (2005)

Studia Mathematica

Similarity:

We prove that for continuous interval maps the existence of a non-empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topological entropy and implies chaos in the sense of Li-Yorke, and we exhibit examples showing that these three notions are distinct.

The topological entropy versus level sets for interval maps

Jozef Bobok (2002)

Studia Mathematica

Similarity:

We answer affirmatively Coven's question [PC]: Suppose f: I → I is a continuous function of the interval such that every point has at least two preimages. Is it true that the topological entropy of f is greater than or equal to log 2?

Topological sequence entropy for maps of the circle

Roman Hric (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A continuous map f of the interval is chaotic iff there is an increasing sequence of nonnegative integers T such that the topological sequence entropy of f relative to T , h T ( f ) , is positive ([FS]). On the other hand, for any increasing sequence of nonnegative integers T there is a chaotic map f of the interval such that h T ( f ) = 0 ([H]). We prove that the same results hold for maps of the circle. We also prove some preliminary results concerning topological sequence entropy for maps of general compact...