Caput Dynamical Systems and Chaos
Faculteit  Science and Engineering 
Jaar  2019/20 
Vakcode  WMMA16003 
Vaknaam  Caput Dynamical Systems and Chaos 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Caput Dynamical Systems and Chaos  
Leerdoelen  At the end of the course, the student is able to: 1. reproduce key properties and phenomenology of standard examples of dynamical systems, such as "the doubling map", "the Henon map", "the horseshoe map", "the solenoid", "circle maps", and relate the qualitative features of such examples to more complex systems. 2. apply key concepts, such as "Poincare maps", "suspensions", "symbolic dynamics", "conjugation", "multiperiodic dynamics", "chaotic dynamics", "dispersion exponents", "persistence of dynamical properties", "attractors", "structural stability", and "KAM theory" to concrete examples of dynamical systems. 3. study a subject from the field of dynamical systems at research level by him/herself guided by the lecturer. 4. give a professional oral presentation on a specific subject from dynamical systems theory and explain the subject to his/her peers (which includes answering questions). 5. relate a specific advanced subject area from dynamical systems theory to a broader context which might also include applications. 

Omschrijving  Dynamical systems theory concerns the question of how deterministic systems evolve in time. This first of all concerns the longterm behaviour of systems which includes stationary, periodic, multiperiodic, and chaotic dynamics, but also transient behaviour is of interest. Moreover bifurcations or transitions between asymptotic states  in particular transitions between regular and chaotic motions  under variation of parameters are of great importance. Special stationary solutions or more generally invariant manifolds can also form the organizing centers for the dynamics in the state space of a dynamical system. Applications of dynamical systems theory range from molecular dynamics to celestial mechanics and extend to the life sciences, climate science, and many other fields. The first half of the course will consist of lectures based on the text book by Broer and Takens, which will provide a solid background. The second half of the course is devoted to studying topics in contemporary research on dynamical systems and their applications. Students will select a topic for giving an oral presentation. The subjects for these presentations may vary from one academic year to the next academic year the course is given. 

Uren per week  
Onderwijsvorm 
Bijeenkomst (S), Hoorcollege (LC), Werkcollege (T)
(The students will give presentations during the tutorials) 

Toetsvorm 
Opdracht (AST), Presentatie (P)
(The final grade is computed as (2H1 + 2H2 + 2H3 + 4P) / 10, where H1, H2, H3, are the grades for the three homework assignments and P is the grade for the presentation. In addition, the grade for the presentation must be 5.5 or higher to pass for the course.) 

Vaksoort  master  
Coördinator  dr. A.E. Sterk  
Docent(en)  dr. A.E. Sterk  
Verplichte literatuur 


Entreevoorwaarden  The course unit assumes prior knowledge acquired from an introductory course to dynamical systems theory like the compulsory course Project Dynamical Systems in the bachelor curriculum.  
Opmerkingen  The material will be tailormade for the projects to be carried out in groups.  
Opgenomen in 
