Admission Requirements
An introductory course to measure theory is advised. If you would like to take the course, but have no knowledge of measure theory, then please contact one of the lecturers.
Description
Ergodic theory is a branch of mathematics that studies dynamical systems from a measure theoretic point of view. Its initial development was motivated by problems from statistical physics. More recent applications include number theory, fractal geometry and combinatorics. A central concern of ergodic theory is the typical behaviour of a dynamical system when it is allowed to run for a long time. Complementary to this typical behaviour is the exceptional behaviour, which usually happens on fractal subsets of the state space. This course focuses on the interplay between these two aspects.
The overall aim of this course is to introduce students to relatively new mathematical research results that merge concepts from ergodic theory and fractal geometry. These results can usually only be known by studying research papers and monographs.
Course Objectives
Course Objectives
Upon successful completion of the course, a student will be able to:
Explain the basic concepts of ergodic theory, including invariant measures, ergodicity, ergodic theorems and entropy.
Explain the basic concepts of fractal geometry, including Hausdorff dimension, iterated function systems, mass distribution principle and Cantor sets.
Analyse the connections between ergodic theory and fractal geometry by finding and studying relevant research literature.
Synthesize the results of the analysis of research literature into an oral and written presentations.
Timetable
The schedule for the course can be found on MyTimeTable.
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
The course consists of two parts. In the first part introductory lectures will be given by Charlene Kalle and Olga Lukina, and students will present solutions to exercises in short presentations.
In the second part students will choose a subject/research article from a list presented at the start of the course and prepare lecture notes for a 45 minute class on the chosen subject and give the lecture. Depending on the number of enrolled students, the projects and presentations may be carried out individually or in small groups.
Assessment method
The grade will be determined by two short oral presentations on homework exercises (20% each), the 45 minute presentation and preparation process (50%) and accompanying handouts (10%).
Reading list
Handouts and research papers will be provided during the course and there will be a list of references to freely accessible lecture notes.
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 more information please email Charlene Kalle or Olga Lukina.
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.