Ben Gurion University of the Negev

Mathematics Department

"Introduction to Symbolic Dynamics"

Spring 2016

Course description

Symbolic dynamics is a branch of mathematics that deals with sequences of characters letters or "symbols" form the point of view of dynamical systems. The basic guiding philosophy is that sometimes it is possible to code and understand complicated systems by a sequence of discrete samples. The decimal expansion of real numbers is a simple example of this kind of procedure. Techniques and ideas from symbolic dynamics have found significant applications in data storage and transmission as well as other parts of mathematics. In this course we will introduce basic notions and results in symbolic dynamics, via interesting examples. We will illustrate relations to other fields and relate to the more general frameworks of topological dynamics and ergodic theory. Basic topics to be covered: Possible additional topics (subject to time, participants background and participants preferences): We will introduce and study the notions of Measure-preserving transformations, Ergodicity, Recurrence The formal prerequisite is basic knowledge of measure theory. The background in other fields (such as functional and harmonic analysis and probability) is not a prerequisite, but will be introduced as needed.

Textbooks and other resources

Grading scheme:

  • The grade will based on a take-home exam (assignment) to be submitted in the end of the course. The assignment will consist of questions that will be given throughout the course.