# MATA310 Introduction to Dynamical Systems (4 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2020-2021, 2021-2022, 2022-2023

## 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.

## Study materials

Luentomoniste jaetaan kurssin aikana.

## 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

**Grading scale:**

0-5

**Evaluation criteria:**

Grading is based on points from exam and weekly exercises

**Language:**

Finnish

**Study methods:**

28h luentoja, 7 harjoituskertaa.

#### Teaching

##### 10/24–12/16/2022 Lectures

##### 12/15–12/15/2022 Exam

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Evaluation criteria:**

Grading is based on points from the final exam

**Language:**

English, Finnish

**Study methods:**

Final exam