One-dimensional dynamics has developed in the last decades into a subject in its own right.
Yet, many recent results are inaccessible and have never been brought together. For this …

Introduction. Consider mixing a deck of n cards by shuffling as usual after turning over one of
the stacks. The resulting permutations are building blocks of the rich dynamics of map**s …

This is intended as a survey article on topological transitivity of a dynamical system given by
a continuous selfmap of a compact metric space. On one hand it introduces beginners to the …

In this paper we shall show that there exists a polynomial unimodal map f:[0, 1]→[0, 1] with
so-called Fibonacci dynamics which is non-renormalizable and in particular, for each x from …

Our aim is to show that the Julia-Fatou--Sullivan structure theory for the dynamics of rational
maps is also valid for smooth endomorphisms of the circle (and of the interval) under …

Our main results, specialized to unimodal interval maps T with negative Schwarzian
derivative, are the following:(1) There is a set CT such that the ω-limit of Lebesgue-ae point …

We consider smooth multimodal maps which have finitely many non-flat critical points. We
prove the existence of real bounds. From this we obtain a new proof for the non-existence of …

We prove that, for an arbitrary rational map $ f $ on the Riemann sphere and an arbitrary
probability invariant measure on the Julia set, Lyapunov characteristic exponents are …

For unimodal maps with negative Schwarzian derivative a sufficient condition for the
existence of an invariant measure, absolutely continuous with respect to Lebesgue …

Metric Attractors for Smooth Unimodal Maps Page 1 Annals of Mathematics, 159 (2004), 725-740
Metric attractors for smooth unimodal maps By JACEK GRACZYK, DUNCAN SANDS, and …