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 …

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 …

In this paper we prove that in any non-trivial real analytic family of quasiquadratic maps,
almost any map is either regular (ie, it has an attracting cycle) or stochastic (ie, it has an …

We construct the “spectral” decomposition of the sets, ω (f)=∪ ω (x) and Ω (f) for a
continuous map f:[0, 1]→[0, 1]. Several corollaries are obtained; the main ones describe the …

Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …

Local Connectivity of the Julia Set of Real Polynomials Page 1 Annals of Mathematics, 147 (1998),
471-541 Local connectivity of the Julia set of real polynomials By GENADI LEVIN and …

Consider real cubic maps of the interval onto itself, either with positive or with negative
leading coefficient. This paper completes the proof of the “monotonicity conjecture”, which …

Rigidity for Real Polynomials Page 1 Annals of Mathematics, 165 (2007), 749-841 Rigidity for
real polynomials By O. Kozlovski, W. Shen, and S. van Strien* Abstract We prove the …

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 …

Equilibrium states for S-unimodal maps Page 1 Ergod. Th. & Dynam. Sys. (1998), 18, 765–789
Printed in the United Kingdom c 1998 Cambridge University Press Equilibrium states for S-unimodal …