We introduce and study a concept which links the Li–Yorke versions of chaos with the notion
of sensitivity to initial conditions. We say that a dynamical system (X, T) is Li–Yorke sensitive …

The Li–Yorke definition of chaos proved its value for interval maps. In this paper it is
considered in the setting of general topological dynamics. We adopt two opposite points of …

There is no recent elementary introduction to the theory of discrete dynamical systems that
stresses the topological background of the topic. This book fills this gap: it deals with this …

A measure-preserving transformation (respectively a topological system) is null if the metric
(respectively topological) sequence entropy is zero for any sequence. Kushnirenko has …

We study multi-sensitivity and thick sensitivity for continuous surjective selfmaps on compact
metric spaces. Our main result states that a minimal system is either multi-sensitive or an …

A subset $ S $ of a topological dynamical system $(X, f) $ containing at least two points is
called a scrambled set if for any $ x, y\in S $ with $ x\neq y $ one has $$\liminf_ {n\to\infty} d …

The notion of chaos in relation to a dynamical system defined by a continuous map was first
used by Li and Yorke [1]. At present, there are so many definitions associated with this term …

We describe various strengthenings of the concept of topological transitivity. Especially
when one departs from the family of invertible systems, a number of interesting properties …

Let $ f: X\to X $ be a topologically transitive continuous map of a compact metric space $ X $.
We investigate whether $ f $ can have the following stronger properties:(i) for each …

The topological structure of minimal sets of continuous maps on graphs, dendrites and
dendroids is studied. A full characterization of minimal sets on graphs and a partial …