Syllabus
Our lecture will be focused on both topological and measure-theoretical dynamical systems. The main attention will be paid to important dynamical phenomena and related results: periodicity, recurrence, minimality and transitivity, complexity measured by topological entropy, invariant measure, measure-theoretical entropy and variational principle, ergodicity and mixing.
All parts will be illustrated by examples.
Annotation
The lecture will offer a self-contained introductory exposition of the theory of low-dimensional discrete dynamical systems. Several principal theoretical concepts and methods for the study of asymptotic properties of an individual trajectory and also the global complexity of the orbit structure will be introduced.
A number of fundamental examples will be discussed.