# MATA310 Introduction to Dynamical Systems (4 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

Basics of discrete dynamical systems. Examples: circle rotations, linear expansive maps of the circle, billiards. Topological properties of dynamical systems, transitivity, mixing, chaos.

## Learning outcomes

The course introduces the basics of discrete dynamical systems and illustrates theory-related concepts through the behavior of exemplary systems. After completing the course the student

• knows what discrete dynamical system means
• knows how to solve basic properties in simple systems
• understands the basics of graphical analysis of dynamical systems and how to apply it
• knows the dynamical properties of basic examples and is able to deduce them
• knows the topological concepts concepts related to dynamical systems and is able to examine those of simple systems
• knows the basics of symbolic dynamics and its application in examining other dynamical systems

## Description of prerequisites

Introduction to mathematical analysis 1-4, Linear algebra and geometry 1, Vector calculus 1.

Vector calculus 2 and Linear algebra and geometry 2 are also recommended.

## Literature

• Katok, Hasselblatt: Introduction to the Modern Theory of Dynamical Systems.; ISBN: 978-0521575577
• Hirsch, Smale, Devaney: Differential Equations, Dynamical Systems, and an Introduction to Chaos; ISBN: 978-0123820105

## Completion methods

### Method 1

Evaluation criteria:
Grading is based on points from exam and weekly exercises
Select all marked parts

### Method 2

Evaluation criteria:
Grading is based on points from the final exam
Select all marked parts
Parts of the completion methods
x

### Teaching (4 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
Grading is based on points from exam and weekly exercises
Language:
Finnish
Study methods:

28h luentoja, 7 harjoituskertaa.

No published teaching
x

Type:
Exam