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

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

No published teaching