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Ergodic Theory and Fractals (BM)


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.


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 of 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.

Course Objectives

The goal 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. Students will study and present (both by writing a small paper/lecture notes, and orally) a for them new part of mathematics.


The schedule for the course can be found on MyTimeTable.

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different

Mode of instruction

Introductory lectures will be given by Kalle and Lukina, all other lectures by the participants. To do this, each participant will choose a subject from the list of subjects presented at the beginning of the course, and then will prepare lecture notes for a 45 minutes class on the chosen subject and give the lecture.

Assessment method

The grade will be determined by active participation (10%) two small oral presentations on homework exercises (20% each) and the 45 minute presentation and accompanying handouts (50%).

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.


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.


For more information please email Charlene Kalle or Olga Lukina.