THEŌRIA DYNAMIKŌN SYSTĪMATŌN
| Title | ΘΕΩΡΙΑ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ / THEŌRIA DYNAMIKŌN SYSTĪMATŌN |
| Code | Θ034 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Panagiotis Batakidis |
| Common | Yes |
| Status | Active |
| Course ID | 600025923 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Spring | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268429
|
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268429
Erasmus
The course is also offered to exchange programme students.
Prerequisites
General Prerequisites
Knowledge of differential manifolds is required. Solid knowledge of general topology is desirable.
Learning Outcomes
- know the basic definitions of the theory of linear dynamical systems and their main characteristics.
- know the definition of the chaotic behavior of a dynamical system and its qualitative/quantitative analysis.
- understand the basic results of bifurcation theory
General Competences
- Apply knowledge in practice
- Work autonomously
- Advance free, creative and causative thinking
Course Content (Syllabus)
Summary of linear theory. Flows, limit sets, non-wandering sets, hyperbolicity, introduction to chaotic systems, structural stability, local bifurcation theory for flows and for diffeomorphisms.
Keywords
Flows, Chaos, Hyperbolicity, Bifurcations
Educational Material Types
- Notes
- Slide presentations
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Reading Assigment | 258 | ||||
| Exams | 3 | ||||
| Total | 300 |
Student Assessment
Description
There will be homework due by the end of the semester together with an oral exam at the end of the semester. These will be accompanied by a small scale written project.
Student Assessment methods
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
Bibliography
Additional bibliography for study
Robinson C. Dynamical Systems - Stability, Symbolic Dynamics, and Chaos (2nd Edition CRC 1999)
Arrowsmith D.K., Place C.M. An Introduction to Dynamical Systems (CUP 1990)
Perko L. Differential Equations and Dynamical Systems (3rd ed. Springer 2001)
Broer H., Takens F. Dynamical Systems and Chaos (Springer 2011)
Guckenheimer J., Holmes P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer 1982)
Last Update
03-12-2024
