Displaying similar documents to “Refinement of the Shannon-McMillan-Breiman theorem for some maps of an interval”

On unimodal maps with critical order 2 + ε

Simin Li, Weixiao Shen (2006)

Fundamenta Mathematicae

Similarity:

It is proved that a smooth unimodal interval map with critical order 2 + ε has no wild attractor if ε >0 is small.

Higher order Schwarzian derivatives in interval dynamics

O. Kozlovski, D. Sands (2009)

Fundamenta Mathematicae

Similarity:

We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives up to some order, obtaining control over derivatives of high order. For a large class of multimodal interval maps we show that all inverse branches of first return maps to sufficiently small neighbourhoods of critical values have their higher order Schwarzian derivatives...

A characterization of ω-limit sets for piecewise monotone maps of the interval

Andrew D. Barwell (2010)

Fundamenta Mathematicae

Similarity:

For a piecewise monotone map f on a compact interval I, we characterize the ω-limit sets that are bounded away from the post-critical points of f. If the pre-critical points of f are dense, for example when f is locally eventually onto, and Λ ⊂ I is closed, invariant and contains no post-critical point, then Λ is the ω-limit set of a point in I if and only if Λ is internally chain transitive in the sense of Hirsch, Smith and Zhao; the proof relies upon symbolic dynamics. By identifying...

Some dynamical properties of S-unimodal maps

Tomasz Nowicki (1993)

Fundamenta Mathematicae

Similarity:

We study 1) the slopes of central branches of iterates of S-unimodal maps, comparing them to the derivatives on the critical trajectory, 2) the hyperbolic structure of Collet-Eckmann maps estimating the exponents, and under a summability condition 3) the images of the density one under the iterates of the Perron-Frobenius operator, 4) the density of the absolutely continuous invariant measure.