# Dynamical Systems and Chaos (ΕΜ5)

### General

School School of Science Department of Mathematics Graduate EM5 1 Dynamical Systems and Chaos Lectures (Weekly Teaching Hours: 3, Credits: 7.5) Special Background - Greek Yes (in English) See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes The course is an introduction to continuous and discrete dynamical systems. Non linear systems of differential equations often lead to non-deterministic (stochastic) results and chaotic situations. The objectives of the course are: Obtaining the theoretical background from the postgraduate student on issues related to dynamical systems described by differential equations. Obtaining the background from the student in computational methods to solve problems of dynamical systems. Description of chaotic situations of dynamical systems Upon completion of the course the postgraduate student will be able to solve with analytical and numerical mathematical methods problems of the dynamical systems and to further deepen their understanding. The course aims to enable the postgraduate student to: Develop the ability to analyse and synthesize basic knowledge of Dynamical Systems. Adapt to new situations Decision-making Working independently Team work All the above will give to the students the opportunity to work in an international multidisciplinary environment.

### Syllabus

Dynamical systems and differential equations of motion, Equilibrium points of the dynamical system, Period doubling of non-linear differential equations, Phase space of the dynamical system, Chaotic trajectory of the system, Poincare map, Applications of the dynamical systems, Henon map, Mandelbrot και Julia sets, Self-similarity under scale change and Fractals. The course includes training in computational methods in the computer laboratory (Applied and Computational Mathematics Laboratory).

### Teaching and Learning Methods - Evaluation

Delivery

In class

Use of Information and Communications Technology

Use of computer lab (Applied and Computational Mathematics Laboratory).

Teaching Methods
Lectures 39
Study study 78
Homework - Projects 70.5
Course total 187.5
Student Performance Evaluation
1. Weekly assignments
2. Final project
3. Written examination at the end of the semester

### Attached Bibliography

• Δυναμικά Συστήματα και Χάος, Πρώτος Τόμος, Α. Μπούντης, 1995, Εκδότης: Α. ΠΑΠΑΣΩΤΗΡΙΟΥ & ΣΙΑ Ι.Κ.Ε.
• Δυναμικά Συστήματα και Χάος, Δεύτερος Τόμος, Α. Μπούντης, 2001, Εκδότης: Εταιρεία Αξιοποίησης και Διαχείρισης Περιουσίας Πανεπιστημίου Πατρών.
• An Introduction to Dynamical Systems and Chaos, G.C. Layek, 2015, Editor: Springer.