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Random Dynamical Systems (BM)


Admission requirements

  • Introduction to Probability (1st year)

  • Introduction to Measure Theory (2nd year)


In this course we will discuss the differences between deterministic
and random dynamical systems, and the new phenomena arrising when the dynamics
is subject to random noise. We plan to discuss the following topics

  • Chaos Game and Iterated Function Systems

  • Products of random matrices

  • Lyapunov exponents

  • Ergodic theory of skew products (cocycles, Abramov-Rokhlin formula)

  • Stochastic stability

Course objectives

  • Learn basic notions in egrodic theory

  • Hyperbolicity, chaotic behavior

  • Notion of Lyapunov exponents,

  • Skew products, understand the difference between quenched and annealed results

  • Phenomenon of stochastic stability


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 timetables into one. This video explains how to do this.  

Mode of instruction

Lectures by Terhesiu, Verbitskiy
Student presentations (at the end)

Assessment method

  • Homework assignments (40%)

  • Final presentation (60%)

Reading list

1) V. Araujo, Random Dynamical Systems,

2) K. Dajani, Introduction to Ergodic Theory,

3) L. Barreira, Lyapunov Exponents. 3- 319- 71261- 1

Relevant research papers will be provided.


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.


Dr. Dalia Terhesiu, d.e.terhesiu[at]