The survey is devoted to the topological dynamics of maps defined on one-dimensional
continua such as a closed interval, a circle, finite graphs (for instance, finite trees), or …

In the paper we consider C 1-smooth self-maps of a cylinder close to C 1-smooth skew
products (and satisfying some additional conditions). We study such geometric property of …

Just below a Period-3 window, the logistic map exhibits intermittency. Then, the third iterate
of this map has been widely used to explain the chaotic intermittency concept. Much …

Let P be a polynomial with a connected Julia set J. We use continuum theory to show that it
admits a finest monotone map φ onto a locally connected continuum [Formula: see text], ie a …

According to a recent paper\cite {bopt13}, polynomials from the closure $\bar {\rm PHD} _3 $
of the {\em Principal Hyperbolic Domain} ${\rm PHD} _3 $ of the cubic connectedness locus …

The connectedness locus in the parameter space of quadratic polynomials is called the
Mandelbrot set. A good combinatorial model of this set is due to Thurston. By definition, the …

A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a
polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like …

Let P be a polynomial of degree d with Julia set J P. Let N˜ be the number of non-repelling
cycles of P. By the famous Fatou–Shishikura inequality N˜≤ d− 1. The goal of the paper is to …

A cubic polynomial with a marked fixed point 0 is called an IS-capture polynomial if it has a
Siegel disk D around 0 and if D contains an eventual image of a critical point. We show that …

W. Thurston constructed a combinatorial model of the Mandelbrot set M 2 such that there is a
continuous and monotone projection of M 2 to this model. We propose the following related …