Admission requirements
Gewone Differentiaalvergelijkingen and Topologie.
Description
In the first part, this course explains basic ideas of the field in low dimensional settings of iterated maps on the line and in the plane. In particular, we develop theory of topological dynamics and hyperbolic dynamics. Important results and ideas in this context that are explained include "period three implies chaos", period doubling route to chaos and the Smale horseshoe map. The second part develops dynamical systems analysis for nonlinear differential equations with emphasis on bifurcations. There are several connections to the first part, in particular, when studying the dynamics and bifurcations of periodic orbits.
The key strength of dynamical systems analysis is the departure from explicit formulas and solution recipes which are replaced by more abstract qualitative techniques from geometry and topology to discuss global properties of solutions. While this modern viewpoint originates in the work of Poincare, it was, in fact, the study of chaotic dynamical systems from the 1960s that lead to a breakthrough in science and an explosion of interest in the field of dynamical systems. Its basic techniques have by now been used in various related settings such partial differential differential equations (which lead to infinite-dimensional dynamical systems) and control theory.
This course will serve as an introduction for the more advanced course "Ergodic Theory and Fractals" and other courses in dynamical systems. The part on continuous dynamical systems complements the modern canon of topics displayed in other courses such as "Introduction to dynamical systems" which has a different focus.
Course objectives
The aim of this course is to introduce the student to basic techniques and results in the broad field of "Dynamical Systems" by developing the theory for two settings: discrete time dynamical systems (generated by maps) and continuous time dynamical systems (generated by differential equations). A second aim of the course is to familiarise students with the ways computers can be used for the exploration and visualisation of dynamical behaviour.
Timetable
In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.
Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.
Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.
Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.
Mode of instruction
Weekly lectures ( 2hrs) and bi-weekly question hours (2hrs)
Assessment method
The final grade consists of homework (20%), project (30%), and written (retake) exam (50%).
To pass the course, the grade for the (retake) exam should be at least 5 and the unrounded weighted average of the three partial grades at least 5.5. No minimum grade is required for the homework or project in order to take the exam or to pass the course.
The homework counts as a practical, it consists of 4 assignments. There is no retake of the homework. The project counts as a practical. There is no retake of the project.
Reading list
The following books are good for references, but not compulsory:
Chaotic Dynamics van Geoffrey Goodson, ISBN 9781316285572
Ordinary Differential Equations and Dynamical Systems van Gerald Teschl, ISBN-13: 978-0821883280
Elements of Applied Bifurcation Theory van Yuri A. Kuznetsov, ISBN 978-0-387-21906-6
Registration
As a student, you are responsible for enrolling on time through MyStudyMap.
In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.
There are two enrolment periods per year:
Enrolment for the fall opens in July
Enrolment for the spring opens in December
See this page for more information about deadlines and enrolling for courses and exams.
Note:
It is mandatory to enrol for all activities of a course that you are going to follow.
Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.
Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.
Contact
for questions you can contact one of the two lecturers.
Remarks
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.