Course title  Dynamical Systems 3 

Course code  KMA/DS3 
Organizational form of instruction  Lecture + Exercise 
Level of course  Master 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  4 
Language of instruction  Czech 
Status of course  Compulsory, Optional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


Course content 
1.Iterated function systems, fractals and fractal dimension 1. Introduction to the subject. Examples of fractals. 2.Iterated function systems, fractals and fractal dimension 2. Prehistory of fractal geometry, Hausdorff and boxcounting dimensions. 3.Iterated function systems, fractals and fractal dimension 3. Iterated function systems (IFS), selfsimilarity dimension, Moran formula. 4.Chaotic dynamics on fractals 1. Hyperspaces, Hausdorff metric, address points, code space. 5.Chaotic dynamics on fractals 2. Transformation from code spaces into fractals, metrics on code space. 6.Chaotic dynamics on fractals 3. Totally disconnected IFS, justtouching IFS, periodic point of IFS. 7.Chaotic dynamics on fractals 4. Discrete and continuous dynamical systems, dynamics on fractals. 8.Homoclinic points, chaos and strange attractors 1. Hyperbolic sets, orbits, pseudoorbits, shadowing lemma. 9.Homoclinic points, chaos and strange attractors 2. Homoclinic points, transversal homoclinic points, chaotic map. 10.Sharkovskij and LiYork theorems. Sharkovskij and LiYork theorems and their application to tent maps. 11.Logistic equation and bifurcations 1. Study of logistic (difference) equation, Feigenbaum constant. 12.Logistic equation and bifurcations 2. Analysis of the Verhulst model, bifurcation diagrams

Learning activities and teaching methods 
Lecture

Learning outcomes 
To introduce the basic results and principles of the theory of chaos and fractals.
Comprehension To uderstand the basic principles of the theory of chaos and fractals. 
Prerequisites 
Knowledge of differential and integral calculus and basic information from the theory of ordinary differential equations to the extent of the course KMA/ODR1.

Assessment methods and criteria 
Oral exam
Credit: the student has to write a course work. 
Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Branch of study Category  Recommended year of study  Recommended semester 

Faculty of Science  General Physics and Mathematical Physics (2014)  Physics courses  2  Winter 